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Leniency Programs and Cartel Prosecution

Leniency Programs and Cartel Prosecution ,N+, NWV,+5WAv W5AWANA, #,+A,A 6 ,W5 ,NW `Lh!?} @Tih , L bb%2 wi?i?U) hL}h@4t @?_ @h|i* hLtiU|L? Btt6N N||B @?_ Wj,j N,N #W 6W,5wc 5 #,W E6W ** h}|t hitihi_ L T@h| Lu |t T@Tih 4@) Mi hiThL_Ui_ ? @?) uLh4 |L| Tih4ttL? Lu |i @|Lh U bbb  L||@ @?_  L*L h?|i_ ? W|@*) ? a*) bbb ,hLTi@? N?iht|) W?t|||i @_@ 6itL*@?@ WDffS 5@? #L4i?UL E6W W|@*) Leniency Programs and Cartel Prosecution Massimo Motta Michele Polo European University Institute, Florence Bocconi University and IGIER, Milan Universitat Pompeu Fabra, Barcelona June 7, 1999 Abstr act W e st udy the enforcement of comp etition p olicy against collusion und er Leniency P rogr am s, which give r ed uced flnes to flrm s revealing in for mation to t he Ant itru st Aut hor ity . S uch programs give flrms an incent ive to break collu sion, but may also have a pro{collusive efiect, since t hey decr ease the exp ect ed cost of m isb ehaviou r. W e analyze the optim al p olicy un der alter nati ve r ules and with homogeneous an d h et erogeneous cartels, obtaining a ranking of the difi er ent schemes and showing when t he u se of r educed flnes may imp rove antitr ust enforcement. W e b eneflted from di scussi ons with Luis Cabral, F ederico G hez zi, Patri ck Rey , Thomas V o n Ung ern{ Ste rnb erg and semi na r parti cipants a t the Unive rsity of Sal erno and the Europ ea n Universi ty Institute (Fi eso le). Thei r co mments a re gra tefull y ac knowle dg ed. 1 Introduction The enforcement of comp etition p olicy against collusion and price flxing agreements is one of the main flelds of antitrust intervention. Recent developments show that the attention devoted by antitrust authorities to collusive agreements has not diminished over time. Recently , the DGIV, the Directorate{ General of the Europ ean Union in charge of comp etition p olicy , has established a sp ecial investigation unit against cartels , and a similar pattern can b e found in the US, where the Antitrust Division of the Department of Justice has reallo cated and improved the resources of the Criminal section in charge for cartel prosecution . In the design of the p olicy we flnd to day richer and more complex mechanisms than those based simply on an increase in flnes. Since 1978 the US Antitrust Division of the Department of Justice has allowed for the p ossibility of avoiding criminal sanctions if sp eciflc conditions o ccurred. In 1993 this p olicy has b een redesigned in the Corp orate L eniency Policy, which establishes that criminal sanctions can b e avoided in two cases: either if a colluding flrm reveals information b efore an investigation is op ened, as it was in the previous regime, or if the Division has not yet b een able to prove collusion when a flrm decides to co op erate . The new Leniency Policy has shown in the flrst years of application a signiflcant success in terms of the numb er of cases that the Division has b een able to op en and successfully conclude. The current EU system draws from the US exp erience. In order to reach a more efiective deterrence of collusive practices, the DGIV has initially fo cused its enforcement p olicy on a sharp increase in flnes: the average flne given to flrms involved in collusion cases, up to the mid Eighties has remained b elow 500.000 ECU while in the last decade it has reached an average of around 1.500.000 ECU . However, if the flrms anticipate a low probability of having collusive practices discovered (and proved), flnes alone will b e insu–cient to prevent flrms from establishing cartels. Although it is hard to quantify such exp ected probabilities, there seems to b e a wide p erception that the deterrence efiects of the flnes has b een relatively p o or, and that v arious typ es of collusive practices are still widespread. This has pushed the Europ ean Union to intro duce a new regime in which reduced flnes can b e given to flrms which co op erate with the antitrust authority by providing evidence of a collusive agreement in which they have b een involved. A 75{100% reduction in flnes can be givenifflrms reveal information b efore an inquiry is op ened, while a lower reduction (50{75%) can b e granted if co op eration o ccurs after an investigation has started, but that investigation has failed to provide su–cient grounds for initiating a pro cedure leading to a decision. A 10{50% reduction in flnes can b e given for partial co op eration, such as providing additional evidence or not contesting the facts on which the Commission bases its allegations. Moreover, only the flrst flrm which co op erates can obtain a reduction, provided that it is not the promoter and ma jor partner of the cartel. It is to o early to ev aluate the efiects of this new p olicy , although the US exp erience suggests that enforcement against cartels might b ecome more efiective. See V enit (1 99 6), p.92 , and Europ ea n Unio n (19 99 , p. 22). See Bi ng man a nd Spratl ing (1 99 5). Some additio na l restricti ons o n the flrms en ti tl ed to b eneflt fro m this regi me a re in tro duced, as the fact that only the flrst can b e gi v en a flne reducti on, and tha t i t must b e a junior partner i n the ca rtel. See F urs e (1 995 ), p. 114 . European Uni on (1 996 ). Notic e that while in the US the regime a ppli es to cri minal sa ncti ons (whi ch include b o th flnes and inca rcerati on), in the E U reducti ons are refe rred only to mo ne tary flne s. Crimina l s anctio ns do no t exis t under EU co mp etitio n law. 1 In this pap er we want to investigate the difierent efiects that the intro duction of a Leniency Program can have on b oth flrms’ b ehaviour and deterrence. Our work is related to other pap ers on the optimal enforcement of law, sp eciflcally those on pre{trial negotiation and settlement and on plea{bargaining , in which these alternative judicial pro cedures have b een studied with a general reference to the US judicial system, although not explicitly to antitrust law. There are however several imp ortant difierences b etween our work and the existing literature. The pap ers on pre{trial negotiation have considered mainly the prop erties of these pro cedures in saving trial costs preventing wasteful litigation. In the plea bargaining literature the enforcer acts more explicitly on b ehalf of taxpayers, balancing the goal of condemning the guilty agents and not condemning the inno cent ones with the minimization of resources devoted to enforcement. In b oth cases, the issue of deterrence is not really addressed: agents have (p ossibly) already committed a crime, and in most pap ers, whether the agent is inno cent or guilty and how strong is the evidence against him (agent’s typ e) is exogenous in the mo del, and it is not explained in terms of incentives to commit a crime. The efiects of the legal pro cedures on preventing the crime or making it to cease are instead at the center of our analysis. In our pap er we are mainly concerned with the deterrence and desistence prop erties of negotia- tions b etween the Antitrust Authority and priv ate flrms. The enforcer is motiv ated by the maximiza- tion of so cial welfare and aims at minimizing the o ccurrence of collusion among flrms by committing on a certain set of p olicy parameters . In order to fo cus on deterrence, in our setting we exclude other ingredients already studied in the literature. First of all we do not consider (v ariable) litigation costs on either party , a central issue in the pre{trial negotiation literature. The enforcer’s budget is set at the b eginning of the game and enforcement costs are sunk, i.e. they are already allo cated among the difierent tasks of the organization, as general monitoring or prosecution. Secondly , we do not consider the p ossibility of wrong sentences, analyzed in the plea{bargaining pap ers: at the end of an investigation either a guilty flrm is condemned or no evidence is reached. In this setting we consider several issues. First of all we analyze the reaction of flrms to difierent p olicy regimes, i.e. on the incentive to collude and on the decision to reveal or not information to the Antitrust Authority . A p erverse efiect can arise under this resp ect: since a Leniency Program allows flrms to pay reduced flnes, it may have ex-ante a pro{collusive efiect, decreasing the exp ected cost of anticomp etitive b ehaviour. But we show that, if the Antitrust Authority has limited resources, and is therefore unable to prevent collusion ex{ante, the use of Leniency Programs can improve the efiectiveness of the p olicy , by sharply increasing the probability of interrupting collusive practices. Hence, in a second b est p ersp ective, flne reductions may b e desirable b ecause they allow to b etter implement ex{p ost desistence from collusion. There is however a third comp onent that op erates in equilibrium: in order to induce flrms to reveal, a Leniency Program has to commit resources to guarantee a su–ciently high probability of indep endent prosecution. This is the implicit cost of a reduced flnes regime, since those resources are subtracted from the general monitoring activity , which determines the frequency of \revelations" and successful inquiries. As the resources committed to prosecution b ecome to o costly , a Leniency The US Leniency Prog ram i nvolves b o th reductio ns of flnes and the el iminati on of the threa t of incarce ratio n. In this pa p er we fo c us o n reduce d monetary flnes. He nce , we use the te rm Leniency P rogr ams in a broa d se ns e. Beb chuk (19 84), Nale bufi (1 987 ), Schwei zer (1 98 9), Shavell (19 89 ). Gr oss man a nd Ka tz (19 83 ), Reing anum (198 8). Othe r pap ers that are rela ted to our own are Ko baya shi (1 99 2) a nd Ma rshall , Muerer and Ri cha rd (19 94 ). 2 Program loses its app eal, and a full flnes regime may b ecome more convenient again. The conditions under which these results hold will b e identifled in b oth a homogeneous and a heterogeneous cartel setting. The efiects and desirability of alternative leniency rules will also b e studied. The pap er is organized as follows. In section 2 we set up the basic mo del, in which every flrm which decides to co op erate with the Antitrust Authority is given a flne reduction. In section 3 we consider alternative Leniency Programs, in which flne reductions can b e granted only if co op eration o ccurs b efore an investigation is op ened, or in which only the flrst comer, or a sp eciflc flrm, is entitled to a reduced flne. Finally , in section 4 we extend the basic mo del to the heterogeneous cartels case. Section 5 concludes the pap er. 2TheModel Throughout the pap er, we assume that the Antitrust Authority (AA from now on) aims at maximizing a utilitarian so cial welfare function and is able to commit to a certain set of p olicy parameters ,which consist of full and reduced monetary flnes and probabilities of enforcement. In the basic mo del of this section we consider a regime in which al l flrms which co op erate in the investigation even aft er this has b een op ened, and which simultaneously provide useful evidence to prove collusion , can b ene flt from a reduction in flnes. In the following sections we shall consider alternative rules and compare them with this b enchmark case. The AA is (exogenously) endowed with a p er{p erio d budget B : in line with the literature, we assume that setting the flnes at any level is not costly , while increasing the probability of enforcement requires resources. More precisely , we assume that the maximum flne that flrms can receive if found guilty of collusion is exogenously given by law and equal to F , a flxed amount of money: then, b eing costless, it is always optimal to set the full flne at this maximum level. However, the AA can commit to a Leniency Program which allows for reduced flnes R • F to flrms which reveal information useful to prove the existence of collusion. Indirectly , that is via the allocation of its given resources among difierent tasks, the AA determines the probability fi of op ening an investigation and the probability p of proving flrms guilty . The former refers to the preliminary activities (general monitoring) necessary to op en an investigation such as collecting information ab out the flrms in the industry , interviewing flrms, suppliers and customers, collecting data from the difierent sources; the latter (prosecution) involves collecting further more fo cused information on the case, ordering surprise \raids" in the flrms’ headquarters, pro cessing the information collected and preparing the case against the flrms according to the existing laws. The AA, allo cating resources to these two groups of tasks can obtain a combinations of these probabilities according to their sp eciflc pro duction functions . The budget Thi s i s in li ne with actual exp erience, in which li ttl e dis cretio n is left by the law to the Autho rity as to the co nditio ns under which reductio ns ca n b e given, and the ir amoun t. Thro ug hout the pap er, w e ass ume tha t informati on g iv en b y a si ng le flrm is enough to prove that a ll the flrms which hav e ta k en part i n the co llusi on are guilty . Thi s mi gh t b e in terpreted a s the cas e where e ach flr m ha s a ccess to the minute s of the meetings whi ch take pl ace a mong al l the co lluding flrms, o r ha s copie s of l ette rs, faxes o r e {mai l mess ages which all the flrms hav e used to co ordinate on the col lusive o utc ome. Since an imp ortant co mp onen t in the w orking of ca rte ls i s the co ordinati on of moves a mong parti cipants, the a ccess of each partner to so me info rmatio n rega rdi ng the others see ms quite real istic . More prec isel y , le t the AA budget c onstraint b e B = w (l + l ); where B is the tota l budg et av ai lable to the Autho rity; fi p l the numb er o f hours all o ca ted to ge nera l mo ni toring and l tho se dev o ted to prose cuti on, w the w ag e rate. In turn, fi p the pro babili te s are determi ne d g iv e n the res ources a ccording to the pro ductio n functi ons fi = k l , and p = k l , with fi fi p 3 constraint is then: B = w fi + w p (1) fi p where w and w are the (constant) unit cost of monitoring and prosecution. W e assume that flrms fi p know the probabilities fi and p chosen by the AA and its budget constraint. The AA ob jective function is a standard utilitarian welfare function, i.e. the sum of pro ducers and consumers surplus. Fines, whether full or reduced, are pure transfers, i.e. they go to the general government budget and are redistributed to consumers without distortions, and cannot b e used by the AA to increase its budget. The agency problem can therefore b e describ ed as cho osing the incentive sche me (R; fi; p) in order to inuence flrms’ b ehaviour and maximize so cial welfare. The incentive compatibility constraints will b e derived from the analysis of the subgame p erfect equilibria in the sup ergame played by flrms once the p olicy parameters are set. After observing the p olicy parameters chosen by the AA, n identical flrms decide whether to collude or not, by correctly taking into account the probabilities (fi; p) and by knowing whether a Leniency Program R is in place or not. W e follow the usual sup ergame literature and consider the incentive of each flrm to play an action which leads to the collusive outcome given that all other flrms take the collusive action. If a flrm deviates it earns a proflt ƒ in the current p erio d but it triggers the punishment of the other flrms, which will play the one{shot non{co op erative equilibrium action forever afterwards, by giving the deviating flrm a total discounted payofi of ƒ + – ƒ =(1 ¡ – ). If instead the flrm decides to take D N the collusive action, then it earns a payofi of ƒ (with ƒ < ƒ < ƒ ) in the current p erio d. M N M D W e assume that the existence of a collusive outcome in the industry is p erfectly observed by the antitrust agency , but this is not enough for collusion to b e proved in courts. T o b e able to build a case against the flrms (which would otherwise win the app eal in a Court), the AA needs to flnd some \hard" information ab out collusion. Such information might consist of any do cument proving that flrms have agreed on prices or have met to co ordinate on the prices to b e charged . Perfect observ ability of collusive prices also implies that the antitrust agency will never op en an investigation on flrms which do not collude at equilibrium. F or simplicity we consider the case where flrms decide once and for all at the initial p erio d whether to collude or to deviate from the pro jected cartel . F rom our disc ussion so far, t he t iming of the game, re prese n t ed in Fi gure 1, is as fol lows: and p 2 [0 ; 1], char acteriz ed fo r simpli city b y p osi tiv e and consta n t ma rginal pro ductivi t y . Then the la b or requirement to obtain fi and p are l (fi)= fi=k and l (p)= p= k re sp ectively a nd the to tal cos t of i mpl emen ti ng fi and p are fi fi p p wl (fi)= w fi=k = w fi and wl (p)= wp=k = w p. It wi ll b e clea r in the ana lys is that assuming de creas ing ma rginal fi fi fi p p p pro ductivi t y , which would i mpl y a concave budg et l ine and a conv ex budget set, w o ul d not a lter all o ur co ncl us ions. T o thi s purp os e, no te tha t in our mo del, l ik e a n y rep ea te d g ame with an inflnite hor izon, there exi sts a contin uum of p os sible e quili br ia, and flrms need so me co ordinatio n to sel ect the full y co ll usi v e outc ome g iving them the p er{p eri o d proflt ƒ . In our s etting, this is not a co mpl etely inno cent a ssumption si nce the ga me b ecomes statio na ry o nl y a fter the i ni tial p erio d, once flrms hav e started c oll uding: co ns idering the cho ice of de via ting for any t> 1 is equiv alent, s ince i n this ca se flr ms , havi ng par ti cipated fo r s ome p erio ds to a ca rtel, pay a n exp ected flne ev en if they devia te later o n. When devi ating i ni ti all y , o n the contrary , a flrm can av o id the flne, si nce it never partici pa ted to the il leg al a greeme n t. Howev er, notice that for this rea son a deviati on at the b eg inni ng is mo re attrac ti v e than bre aking down the cartel l ater o n, and the as so c iated co ns tra ints ar e more stringent. Since the a lternative cas e makes the a na lysis more complex but g iv e s the sa me quali tative res ul ts, we have preferred to k e ep the si mpl est v ers ion where flrms decide only a t t = 1 whether to devi ate or col lude. 4 t = 0 The Antitrust Authority determines the p olicy parameters R; fi; p, which are observed by all flrms. The reduced flne R is granted to any flrm co op erating even after the investigation is op ened. t =1 Firms i =1; ::; n decide whether to collude or deviate and realize the p er{p erio d asso ciated payofi. t = 2 The AA op ens an investigation with probability fi 2 [0; 1]. If the inquiry is not op ened, each flrm realizes the p er{p erio d proflts asso ciated to the previous choice. If the investigation starts, flrms simultaneously decide whether to reveal information that the AA will flnd useful to prove collusion; if at least one flrm reveals, the AA is able to prove them guilty . The flrm(s) which co op erated with the AA pays R • F while the others pay the full flne F . If no flrm reveals, the AA is able to prove them guilty with probability p 2 [0; 1]. If the AA has not b een able to prove the flrms guilty of collusion at the end of this inquiry , the flrms will never b e investigated again in the future. If proved guilty , they will b ehave non{co op eratively forever in the future. t> 2 If up to the previous p erio d the AA has not started an investigation, with probability fi it op ens an inquiry in t, flrms decide whether to reveal, and so on. F igure 1 ab out he re W e can now solve for the equilibrium of this game. Our flrst step is to identify the incentive compatibility constraints, which requires to work out, for given p olicy parameters, the subgame p erfect equilibria of the game starting at t = 1, characterized by flrms colluding or deviating and by the choice of revealing or not information to the AA. W e flrst consider the \revelation game" which is played from t = 2 on if an investigation is op ened by the AA. The following Lemma identifles the conditions for the existence of Nash equilibria in which flrms co op erate or not with the AA. Lemma 1Let (1 ¡ p)(ƒ ¡ ƒ ) M N 1 ¡ · – ( p; F ; R)(2) pF ¡ R Pr ovide d that an investigation has b e en op ene d, in the \r evelat ion" game an e quilibrium al way s exist s in which al l flr ms r eve al information. If 1) pF < R or 2) pF ‚ R and – ‚ – (p; F ; R) an e quilibrium exist s in which no flr m r eve als. If this latter exist s, it Par eto dom inates t he e quil ibr ium outc ome in w hich the flrm s r eve al . Pr o of: Se e App endix. 2 5 ~ Figure 2.a b elow illustrates the critical lo cus of p oints –: T o the right of this curve, flrms reveal if an investigation has b een op ened by the AA. T o the left of it, they do not. This curve, which always passes through the upp er right corner of the picture, rotates to the left as the reward from revealing information increases (that is, the lower R) and the larger b ecomes the flne F to b e paid if found guilty: in other words, revelation o ccurs for a wider set of parameters as the incentive to co op erate with the AA is sharp ened. W e can now consider the initial decision to join the prop osed agreement or deviate at t=1. Three p ossible outcomes can o ccur: flrms might prefer not to collude (NC ), since they exp ect an immediate deviation. Alternatively , collusion may start, followed by the decision not to reveal (CN R) or to reveal (CR) if an investigation is op ened by the AA. T o simplify the statement of the results, it is convenient to intro duce the following expressions. – (fi; p; F ) is the v alue which solves: NC –fi(1¡p) ƒ (1 + )+ –fip( ¡ F ) M – ƒ 1¡– 1¡– =ƒ + (3) 1 ¡ – (1 ¡ fi) 1 ¡ – while – (fi; R) is: CR ƒ ¡ ƒ D M · – (fi; R): (4) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N The following prop osition identifles the conditions on the discount factor – for the three outcomes to o ccur. Prop osition 2 For given p olicy p ar ameters (F ; R; fi; p) : † if – (fi; R) • – • – (p; F ; R), fl rms c ol l ude and r eve al if monitor e d (CR). CR † if – ‚ maxf– (fi; p; F ); – (p; F ; R)g, flrm s c ol lude and do not r eve al if monitor e d (CN R). NC † if –< mi nf– (fi; p; F );– (fi; R)g flrm s do not c ol lude (NC ). NC CR Pr o of: See App endix. 2 Figure 2.a b elow illustrates the line corresp onding to – , for given v al ues of fi and R: this CR lo c us do es not dep e nd on p (it is †at) sinc in the region to the right of – flrms co op erate with the AA once an investigation is op ened and p b ecomes irrelev ant. Ab ove the line, flrms prefer to collude even though they anticipate that, if an investigation is op ened, collusion would collapse b ecause flrms would reveal information to the AA. Below the line, flrms, anticipating revelation, prefer to deviate, and the collusive outcome never o ccurs. Consider now – , which identifles the regions where flrms start colluding (ab ove) or not (b elow). NC ƒ ¡ƒ D M For fi =0 of p =0, we have – = – = , and the condition for collusion amounts to NC CR ƒ ¡ƒ D N the \textb o ok" critical discount factor, which is in fact derived under the condition of no antitrust enforcement. Positive v alues of fi and p (and higher v alues of the full flne F ) inc re ase – and make CR the cartel harder to sustain, since the exp ected collusive proflts are reduced. 6 Note also that the more generous the Leniency Program (the lower the reduced flne R)the lowe r – : if flrms exp ect that in case an investigation is op ened they have the p ossibility to reveal CR information and get away with a small flne, this will give an incentive to cho ose the collusive strategy . In other words, a generous Leniency Policy might stimulate ex{ante collusion. (W e shall come back to this issue b elow.) Figures 2.a and 2.b ab out here The curves represented in Figure 2.a deflne, for a given fi, the conditions that must hold for a collusive agreement to emerge, and those which induce revelation or not if an inquiry is op ened by the AA. More precisely , if no Leniency Program is intro duced (R = F ) flrms have no reason to reveal information to the Authority if an investigation is op ened, and the equilibrium outcomes would b e deflned uniquely by the line – : Ab ove the line, flrms would collude (CNR); b elow, they would not NC (NC), b ecause any prop osed agreement would break down immediately . Reduced flnes mo dify the situation: in the region to the left of – flrms don’t reveal if monitored, and the same argument ab ove still applies. T o the right of that curve, flrms anticipate that they reveal information if monitored: below – they prefer not to collude and ab ove they initially collude and then reveal if monitored. CR W e can notice that the conditions for collusion are more demanding with resp ect to the standard case when no AA op erates: the critical discount factor needed for a collusive outcome is always higher than (ƒ ¡ ƒ )=(ƒ ¡ ƒ )when fi and p are p ositive. When a flrm considers whether to join a cartel D M D N or deviate, in fact, it ev aluates the collusive proflts taking into account that with a certain probability collusion will b e detected, inducing a double loss: the flne to b e paid and the lost collusive proflts from there on. The higher the probability of these losses, the lower the collusive proflts. Hence, we need a higher and higher discount factor to balance the temptation to deviate. T o understand the role of Leniency Programs on the sustainability of collusion, consider what happ ens when, starting with a situation in which no Leniency Program is used, we intro duce reduced flnes. This has two efiects which are shown in Figure 2.a. On the one hand, the Leniency Program might have an adverse, pro{collusive efiect. By reducing the exp ected v alue of the flne to b e paid if an investigation is op ened, the Leniency Program might give an incentive to collusion. This o ccurs in the area (1) included b etween the dotted part of the curve – and the line – . In this region, no NC CR collusion can b e sustained in the industry if full flnes are given (NC), but under a Leniency Program flrms would engage in collusion and, if monitored, they would reveal (CR) and pay the reduced flne R< F . On the other hand, there exists an area (2) where collusion will break down (b ecause the flrms reveal information) if the AA starts monitoring the industry (CR), whereas in the absence of a Leniency Program collusion could stop only after a successful complete investigation (CNR). This is the area comprised b etween the dotted part of the curve – and the curve – . . NC W e can now move to the analysis of the optimal p olicy , having identifled the implementable allo cations. So far we have expressed the conditions for the difierent equilibrium outcomes in the If the Le ni enc y P rogra m w e re una n tic ipated, flrms would decide whe ther to co llude or no t on the ba sis of an exp ected flne R = F and therefore w o ul d not co o p erate unl ess – ‚ – . When the l eni ency progra m is intro duc ed une xp ectedly , N C co llusio n w o uld break down in all the area b el ow the curv e – (that is , (1 ) plus (2)), without an y adv ers e efiec t ari sing. 7 space (p; – ): this was useful b ecause we obtained the conditions of cartel stability in terms of critical discount factors, thereby allowing a comparison with the mo dern theory of collusion. T o pro ceed with the analysis of the optimal p olicy design, it is convenient to rewrite the critical lo ci found ab ove in the spac e (p; fi) of p olicy parameters. Firms would reveal if monitored if: ƒ ¡ ƒ + R(1 ¡ – ) M N p ‚ =~ p( –; R ; F ): (5) ƒ ¡ ƒ + F (1– ) M N Firms would prefer to collude rather than deviate, when they anticipate that the op ening of an investigation would result in collusion broken down by revelations, if: ƒ ¡ ƒ + – (ƒ ¡ ƒ ) M D D N fi • = fi (–; R): (6) CR – (ƒ ¡ ƒ + R) D N Finally , collusion arises in the case where flrms anticipate that no revelation would o ccur after the op ening of an investigation, if: (1 ¡ – )[ƒ ¡ ƒ + – (ƒ ¡ ƒ )] M D D N fi • = fi (–; p; F ): (7) NC – [ pF (1 ¡ –)+ p(ƒ ¡ ƒ )+ ƒ (1 ¡ – ) ¡ ƒ + – ƒ ] M N D M N The three lo ci ab ove allow to deflne, in the space of p olicy parameters, three regions asso ciated with difierent implementable allo cations, in which flrms do not collude (NC), collude and reveal if monitored (CR) and collude and do not reveal (CNR): A = f(fi; p) 2 [0; 1] j fi ‚ maxffi (p);fi gg (8) NC NC CR A = f(fi; p) 2 [0; p ~ ] £ [0; 1] j fi< fi (p)gg (9) CN R NC A = f(fi; p) 2 [0;fi ] £ [~ p; 1]gg (10) CR CR When no Leniency Program is intro duced the only outcomes are NC, if (fi; p) are ab ove the fi NC curve, or CNR otherwise. If R< F the threshold p ~ b ecomes lower than 1 and CR is an outcome if fi< fi and p> p ~ . Notice that fi (~ p)= fi , that is the upp er left corner of the region asso ciated CR NC CR to CR shifts up along the fi curve as R is reduced. When R = 0 we obtain the widest CR region. NC W e flnd also in the (fi; p) space the same adverse efiect of Leniency Programs already discussed: the intersection of A when R = F and A when R< F is non empty . That means that there are NC CR p olicy combinations which prevent collusion when full flnes are given and that induce flrms to collude and reveal once a Leniency Program is intro duced. ƒ ¡ƒ D M Moreover, if –< , where the latter term is the standard critical discount factor for col- ƒ ¡ƒ D N lusion when no antitrust prosecution is considered, fi < 0and fi < 0, i.e. the only admissible NC CR outcome for any v alue of the p olicy parameters is NC. Figure 2.b illustrates the equilibrium outcomes ƒ ¡ƒ D M when –> and R< F , and it is the dual of flgure 2.a - see ab ove. ƒ ¡ƒ D N W e summarize the subgame p erfect equilibrium outcomes of the sup ergame played by flrms for given p olicy parameters and discount factor – in the following prop osition, which is the dual of Prop osition 2. Prop osition 3 Given t he gains ƒ and ƒ s p e cifle d ab ove, M D 8 † If the p ol icy c ombination (fi; p) 2 A ther e is a un ique sub game p er fe ct e quilibrium in which NC flr ms wil l abstain ex{ant e fr om c ol l usion ( NC). † If (fi; p) 2 A t her e is a unique sub game p erfe ct e quilibrium in which flrm s c ol lude and don ’t CN R r eve al if m onitor e d (CNR). † If (fi; p) 2 A ther e is a unique sub game p erfe ct e quilibrium in which flr ms c ol lude and r eve al CR if monit or e d (CR).If R = F , A is an empty s et . CR The AA cho oses (fi; p; R)given the incentive compatibility constraints, summarized in Figure 2.b and Prop osition 3, in order to maximize a utilitarian welfare function in which flnes are pure transfers. Let K = DW L=(1 ¡ – ) b e the discounted sum of the deadweight loss DW L, which can b e thought of as the net so cial b eneflt from ppreventing collusion Moreover, let W b e the present v alue of the welfare gain if the p olicy induces the equilibrium outcome j = NC; C R; C N R. Then we have, for given (fi; p), W = K> W = fiK =(1 ¡ – (1 ¡ fi)) >W = fipK =(1 ¡ – (1 ¡ fi)). NC CR CN R It is useful to identify the (welfare) indifierence curves for the p olicy problem in the (fi; p) space: if we do not intro duce flne reductions, in all the region A we have full deterrence ex-ante and the NC asso ciated welfare gains are K for all the p olicy parameters in the A re gion. In t he re gi on A NC CN R the indifierence curve for a level of welfare gains W is fi = W (1 ¡ – )=(pK ¡ – W ), i.e. it CN R CN R CN R is a decreasing and convex curve in the (fi; p) space: ex{p ost desistence in this case dep ends on b oth fi and p according to the trade{ofi describ ed by the curve. F igure 3 ab out he re Moreover, it is easy to show that the indifierence curves in the A region have a shap e similar CN R to the fi curve as deflned in ( 7), which is the upp er b oundary of that region, and in the limit they NC overlap with that curve. In fact, if we consider the indifierence curves for given W and the fi (p) CN R NC curve which is the upp er b oundary of the A region and equate them we obtain after rearranging: CN R W – (ƒ ¡ ƒ ) ¡ (ƒ ¡ ƒ ) CN R D N D M = · p ^ K – (F (1 ¡ –)+ ƒ ¡ ƒ ) M N The right hand side expression corresp onds to the upp er intercept of the fi (p) curve at fi =1, NC i.e. fi (^ p) = 1. Hence, lo oking at the expression ab ove, if W =^ pK the indifierence curve NC CN R overlaps with the upp er b oundary of the A region, that is with the fi (p). F or W < pK ^ CN R NC CN R the indifierence curve in the A region shifts toward the origin. CN R When a Leniency Program is intro duced, b elow the A region we have the A and A NC CR CN R regions. The indifierence curves across the region A are fi =(1 ¡ – )W =(K ¡ – W ): those CR CR CR curves are horizontal, since in the CR case ex{p ost desistence dep ends only on fi. The same level of welfare in the A region can b e obtained only if fi is higher; that means that the indifierence curve CN R is discontinuous at p ~ and jumps up as we move from the A to the A region . CR CN R Notic e that W = W fo r the s ame fi when p = 1 . Hence, i f we extend the W indi fierence curve in the A CN R CR CN R CR reg ion up to p = 1 we flnd the level o f fi such that W = W and we are able to iden ti fy the l ev el of the indi fie renc e CR CN R curv e in the A regi on, as shown in flg ure 3. CR 9 The iso{welfare curves in the A and A regions do not identify a convex set of p olicy CN R CR parameters. W e pro ceed therefore convexifying the indifierence curves in the following way . Consider an indifierence curve in the A and A region; draw a line which passes through the p oint of CN R CR discontinuity (fi =(1 ¡ – )W =(K ¡ –W );p =~ p) and which is tangent to the indifierence curve in CR CR the A re gion. Le t t he tange nc y p oi nt b e e(W ); rep eating this precedure for difierent v alues CN R CN R of W an entire lo cus e(W ) is obtained. Deflne E the subset of A to the left of that CN R CN R CN R CN R lo cus, which is represented in Figure 3. Notice that, constructing E , we have excluded those CN R p oints on the indifierence curves in the A region which are dominated by a combination of p olicy CN R parameters in (at the b oundary of ) the A region, obtaining a convex set of p olicy parameters. CR W e can now analyze the optimal p olicies. According to the v alues of B; w and w , i.e. the fi p p osition of the budget constraint B = w fi + w p in the (fi; p) space, we can have difierent solutions fi p to the optimal p olicy problem. Prop osition 4 Con sider the optimal p olicies given the budget c onstr aint. † If the budget c on str aint is ab ove or on the fi (p) cur ve, the optimal p olicy implements NC at NC a tangency p oint b etwe en the budget c onstr aint and the fi (p) curve, and the set of p ossible NC e quilibrium outc omes incl udes al l the cur ve, i.e. E = f(fi; p) j p 2 [0; 1];fi = fi (p)g. NC NC † If the budget c onstraint is b elow the fi (p) curve the optimal p olicy implements either CR or NC CNR. { In a CR e quilibrium the optimal p olicy sets R =0, p =~ p and fi along the budget constr aint, and the p olicy c ombinations lie along the vertic al line p ~,i.e. inthe set E = f(fi; p) j fi 2 CR [0;fi ];p =~ pg. CR { In a CNR e quilibrium the optimal p olicy combinations are at the tangency p oint b etwe en the budget c onstraint and the indifierenc e curve. † If the budget constr aint is tangent to an indifier enc e curve in the E re gion deflne d ab ove, CN R the optimal p olicy implements a CNR outc ome; otherwise CR is the e quilibrium outc ome. Pro of: See App endix. 2 Prop osition 4 gives the conditions which in general allow to identify the optimal p olicies for given budget constraint and it deflnes three sets of p olicy parameters which corresp ond to the difierent equilibrium outcomes, as represented in Figure 3. It is useful to consider the sequence of p olicy regimes that are asso ciated with lower and lower budget constraints. Notice that two p ossibile sequences can arise, according to the way in which the budget constraint shrinks: either we move from a NC to a CNR regime, if the budget constraint is initially very steep and the tangency p oint on the fi (p) NC curve which implements the NC outcome lies in the neighb orho o d of the E region, or we have, CN R for atte r budget constraints, a NC-CR-CNR sequence if the tangency p oint with the fi (p)curve NC is in its lower part. This latter case seems quite interesting and allows to get the intuition of the pros and cons of the Leniency Programs. Consider the optimal p olicies for parallel shifts of the budget constraint; for a relatively high total endowment a NC outcome can b e implemented at a tangency p oint with the fi (p)curve: in NC 10 this case reduced flnes would b e harmful, inducing collusion (and revelation) when otherwise the AA would b e able to prevent collusion. When the budget constraint shifts downwards and lies b elow the A curve, it is no longer p ossible to obtain ex-ante deterrence of collusion. In this case it is optimal to NC implement a CR outcome by granting maximum flne discounts and setting the p olicy parameters along the p ~ vertical lo cus: intuitively , when the AA is only able to implement ex-p ost desistence, reduced flnes b ecome app ealing as a less costly way of proving and interrupting collusion. The implicit cost of such a p olicy is the need to sink resources in order to make indep endent prosecution a credible threat which induces revelation. As a consequence, when the total endowment is further reduced (the budget constraint shifts further downwards), fewer and fewer resources are left for general monitoring, which in the end determines the likeliho o d of interrupting collusion and the desirability of such a p olicy . At some p oint, we flnd that the (low) budget constraint b ecomes tangent to the iso{welfare curve in the E region: it means that we obtain a higher exp ected welfare moving to the region where CN R flrms collude and do not reveal, abandoning the Leniency Program and changing the mix of p olicy parameters in a more favourable way . 3 Alternative Leniency Rules In this section we adapt the model to alternative Leniency Rules that have b een adopted in the recent exp erience in the US and in the Europ ean Union. The flrst extension refers to the p ossibility of giving reduced flnes only if flrms reveal information b efor e an inquiry is op ened by the AA. Another regime assigns the reduction in flnes only to the flrst flrm which ofiers co op eration with the agency . Next, we suggest that if only one sp e ciflc flrm is entitled to b eneflt from a Leniency Program, this p olicy would b e even more successful. 3.1 Fine reductions only before the inquiry is opened As mentioned in the intro duction, the initial Leniency Program intro duced in the US in 19 78 entitled flrms with a reduction in flnes only if the co op eration started b efore an inquiry was op ened. On the same line, the actual regime chosen in the EU with the July 1996 Notice is more favourable for flrms who reveal information b efore the AA has op ened an o–cial investigation. It is therefore interesting to analyze whether this rule can b e justifled in terms of enforcement efiectiveness. W e show that this is not the case. Let us consider a \flne reductions only b efore an inquiry is op ened" regime. The corresp onding game structure is describ ed for the general case of n flrms in the following : t = 0 : The AA sets the p olicy parameters fi ; p; R which are observed by the flrms. t =1 : Firms i =1; : :; n decide whether to collude or deviate and realize the asso ciated payofis. t = 2 : At the b eginning of the p erio d, flrms simultaneously cho ose whether to reveal the existence of the cartel to the AA, b enefltting of reduced flnes, or not; if no flrm reveals, the AA op ens an investigation with probability fi 2 [0; 1], provi ng t he m gui lty wit h probabil ity p 2 [0; 1]. Then, payofis are realized. The pay ofis in the di fie ren t o utco mes a re s imil ar to the mo del a na lysed ab ove, and wil l b e o mitted he re in the descri ptio n o f the ga me. 11 t> 2 : if up to the previous p erio d the AA has not started an investigation, the game restarts as from t = 2, etc. Consider flrst the subgame starting at t = 1 after a decision to collude. T o flnd the conditions under which not revealing is an equilibrium, we have to compare the payofi from revealing when the other flrms do not reveal, namely ¡ R, with the payofi from not revealing when the other flrms 1¡– do not reveal. The latter is given by: ƒ ƒ N M ƒ = fi[p( ¡ F )+(1 ¡ p)( )] + (1 ¡ fi)(ƒ + – ƒ ); nr nr 1 ¡ – 1 ¡ – whence: ƒ ƒ N M fip( ¡ F ) + [(1 ¡ – + fi( – ¡ p)] 1¡– 1¡– ƒ = : nr 1 ¡ – (1 ¡ fi) ƒ ƒ N M It is simple algebra to check that this payofi is higher than (p( ¡ F )+ (1 ¡ p) ), the 1¡– 1¡– exp ected payofi from not revealing after the investigation has b een op ened, which was the relev ant one under the rule analyzed in the previous section. Since the payofi from revealing is the same in b oth cases, it follows that the equilibrium where flrms do not reveal is more likely to o ccur when the Leniency Program is applied only for revelations b efore the inquiry is op ened. In other words, the curve – moves to the right and collusion is less likely to b e broken by revelations in this regime. This is hardly surprising, b ecause the probability of the event \b eing found guilty and thus flned" is lower b efor e seeing if the industry will b e monitored than after an investigation is actually op ened. W e have now to consider if the Leniency Program might change the ex{ante incentives of flrms to collude. It turns out that there would never b e collusion in the industry when flrms exp ect that there would b e revelation of information to the AA in the following p erio d: this implies that an equilibrium in which flrms cho ose to collude and reveal do es not exist. In fact, by colluding when exp ecting the cartel to b e broken by information given to the AA, a flrm would get V =ƒ + – (ƒ =(1 ¡ – ) ¡ R). c M N By deviating, it would get V =ƒ + – ƒ =(1 ¡ – ) . Si nce ƒ > ƒ and R ‚ 0, it follows that d D N D M V <V . c d In the case, considered in the previous section, where flrms were entitled to flne discounts aft er the op ening of an investigation, the exp ected proflt from collusion decreases when the event \op ening of an investigation" realizes, leading flrms to reveal information to the agency . In the case we are considering here, instead, nothing new happ ens b etween the moment when the flrms decide on collusion and the moment when they are asked to co op erate with the authorities to break down the cartel. Our analysis reveals that if Leniency Programs are to b e efiective in breaking down cartels, they should b e extended to b eneflt flrms which reveal after the industry is put under monitoring. Since proving flrms guilty of collusion is a very lengthy and complex issue, which do es not always end up with the flrms b eing condemned, a great amount of resources can b e saved and a flnal p ositive outcome guaranteed by ensuring that flrms have the prop er incentives to collab orate with the AA even after an investigation has b een started. Allowi ng flrms to cho ose whethe r to reveal or no t b e fore an inv es tiga tion i s op ened at a n y p erio d w o ul d not cha ng e the res ul ts. 12 This result is consistent with the US exp erience, where initially the Leniency Program was used only for flrms which sp ontaneously ofiered evidence b efore the inquiry was op ened by the AA. In this initial regime the program was quite inefiective while, once allowed in 1993 for reduced flnes even after the inquiry was op ened, the numb er of cases in which flrms co op erate with the judges increased signiflcantly . In the 1994 Annual Rep ort of the Antitrust Division it is stressed that in the flrst year of the new regime \an average of one corp oration p er month come forward with information on unilateral conspiracies, compared to an average of one p er year under the previous p olicy . The p olicy thus allowed the Division to extend the reach of its criminal enforcement activities with relatively little exp enditure of resources" . According to our results, the new regulation on Leniency Programs adopted by the EU should b e widened. The regulation states that flrms which denounce a cartel b efore the Commission has op ened an investigation are entitled to a reduction of 75{100% of the flnes. Firms which denounce a cartel after that a \veriflcation" has b een op ened are entitled to a 50{75% reduction of the flnes, but only if those veriflc ation s had not b e en fruitful and had not led to the op ening of a pro cedure. Basically , this means that Leniency Programs are op ened only for flrms op erating in industries which are not under the scrutiny of the AA. This narrows to o much the scop e of the application of the regulation, and fails to provide the flrms with enough incentives for revealing information which can b e useful to break the cartel. 3.2 Only the ¯rst comer obtains a ¯ne reduction The criteria that determine which flrms can receive the b eneflts of a reduced flne have b een restricted in difierent ways b oth in the US and in the EU exp erience. An interesting case is where only the flrst flrm which ofiers evidence is given a flne reduction, as it is the case in the EU regulation. In this case the game structure is the same as in our initial mo del. The only difierence is that if all flrms decide to reveal information to the judges, as it happ ens in a subgame p erfect equilibrium in which flrms reveal if monitored, the exp ected payofi b ecomes: ƒ R +(n ¡ 1)F ¡ (11) 1 ¡ – n where n is the numb er of flrms in the cartel: every flrm is ex{ante the flrst one to disclose information to the AA with probability 1=n. Notice, however, that when we check for the existence of an equilibrium in which no flrm reveals, a deviating flrm obtains the reduced flne R for sure, b eing the only one which co op erates with the judges. Hence, the condition for an equilibrium in which no flrm reveals is – ‚ – , exactly as in the case treated ab ove. Moreover, it is easy to see that if an equilibrium exists in which no flrm reveals if monitored, it also Pareto dominates the equilibrium in which all flrms co op erate with the AA. Anti trust Divi sio n (19 94), p.6 {7. See O–cial Journal of the Europ ean Communities , Seri es C, 2 07, 1 8{ 7{1 998 . T a ken litera lly , o ur anal ys is wo ul d al so sugg est tha t when flrms reveal they s ho ul d al ways recei ve a zero flne ( R =0), si nce this wo ul d gi ve them the g reates t incentive to deno unce the ca rtel. Howeve r, we a re a ssuming tha t co lla b orati ng wi th the AA is a binary v ari able. E ithe r o ne do es not coll ab ora te, or i f it do es i t ca n g ive a ll the info rmatio n necess ary to prove the pa rticipa ti on in the cartel of all the flrms . In rea lity , the typ e of info rmatio n that flrms ca n provide would b e more of a continuo us v ari able, and tuning the flne re ductio ns to the quali ty of the info rmatio n reveal ed make s sense. 13 ~ Consider now the decision of flrms on collusion at t =1: if – ‚ – flrms will not reveal if monitored and everything is as in the basic mo del. However, if –< – , revelation will follow the op ening of an investigation, but flrms’ incentives to collude are mo difled in the present regime, since the exp ected payofi if monitored is lower than in the previous case where all flrms could b eneflt from the Leniency Program. One can check that flrms will abstain from collusion ifi ƒ ¡ ƒ D M – ‚ eq ui– (12) CR R+(n¡1)F (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fi( ) D N It is immediate to notice that – <– , that is, the region of parameters that induce flrms to abstain CR CR from collusion is larger than in the previous \all flrms get the reduction" regime | see Figure 4. F igure 4 ab out he re The intuition of this result is as follows: in the more restrictive set of rules analyzed in this section, the exp ected reduction in flnes is smaller when all flrms cho ose to coop erate with the judges, although it is equiv alent when we consider the incentive for a flrm to cheat the partners when they do not reveal. Hence, when flrms anticipate that they all will confess if monitored, they exp ect higher sanctions. Consequently , in some cases they flnd it less attractive to collude and re ve al as an alternative to deviating from the b eginning and avoiding the flne. The regime therefore is able to partially reduce the ex{ante incentive to collusion without reducing the p ower of the program in making flrms denounce a cartel after an inquiry is op ened. This case suggests an alternative rule which might increase the efiectiveness of a Leniency Program, by further reducing the ex{ante incentive of engaging in collusion induced by the exp ected reduction in flnes. 3.3 Only a speci¯c ¯rm receives a ¯ne reduction As we have rep eatedly emphasized, a Leniency Program inuences flrms in two ways. The flrst is that it stimulates ex{p ost breaking of the cartel via revelation of information to the AA; the second (adverse efiect) is to increase the incentive of collusion via a reduction in the punishment in case of b eing found guilty . W e have also seen that granting a reduction in flnes only to the flrst flrm which reveals works b ecause it leaves unchanged the flrst efiect but reduces the second. The efiectiveness of the Leniency Program could b e increased even further by increasing asymmetries in the industry and sp ecifying ex{ante that only a sp eciflc flrm could b e entitled to the LP , no matter the way in which such a flrm is selected. The way of interpreting this rule is that of deflning ex{ante a set of parameters which allow all the participants in each sp eciflc situation to identify a single flrm entitled to a reduced flne : the flrms involved in the cartel, applying the rule, are able to work out which one will b e the flrm selected. Denote this flrm with a numb er, say 1. The conditions under which revelation o ccurs are the same as usual: If –< – , the cartel would break b ecause flrm 1 denounces it. On the other W e thank P . Rey fo r s ug ges ti ng this extensio n. F or insta nce, i t mi gh t b e the flrm lo cated in the smal lest city , o r the l ast one in a lpha b etica l o rder, etc. 14 hand, the conditions under which ex{ante collusion o ccurs will change. F or the n ¡ 1 flrms which are not entitled to the Leniency Program, the condition for taking part in the collusion will b e: ƒ ¡ ƒ D M – ‚ · – (13) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiF D N F or flrm 1, the c ondit ion is laxe r: ƒ ¡ ƒ D M – ‚ (14) (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N However, since all the flrms must flnd it convenient to take part in collusion, the latter condition does not play any role, while the former is binding and determines the existence of collusion. Also, F I notice that – >– >– | see Figure 4. In other words, if the authority targets the Leniency CR CR CR Program to a sp eciflc flrm, it will b e able to reduce the ex{ante adverse efiect of it without decreasing the ex{p ost incentive to reveal information. Hence, collusion b ecomes less likely b ecause the flrms excluded from the program flnd it less app ealing to engage in a cartel which includes a likely cheater . 4 Heterogeneous Cartels So far we have considered homogeneous cartels, in which the payofis in each p ossible outcome were the same across partners. Notice however that, in all our arguments, if the participants have heterogenous payofis and they know the payofis of the partners in each p ossible outcome, the equilibria are governed by the conditions of one of the flrms, the one whose constraints bind. This decisive agent is the p oint of reference for the others, whether they exp ect such flrm to deviate or to reveal information after colluding, and drives the equilibrium conditions of the entire cartel. Hence, in a sense, our previous analysis allows to consider heterogeneous flrms within a cartel, but it assumes that in each cartel in the economy such a decisive agent is always the same. It is therefore interesting to consider the case in which the cartels are truly heterogeneous, in the sense that the participants may difier in payofis and the decisive partner may b e difierent across cartels. W e consider in this setting the design of an optimal enforcement p olicy which cannot b e made conditional on cartel’s typ e, due to informational and/or institutional restrictions. Hence, the AA has to design a single, general p olicy facing many difierent industries, characterized by heterogeneous market conditions and p otential gains from collusion. In this case, the p olicy implemented will induce difierent efiects in the v arious industries, reaching a more or less efiective deterrence of collusion and inducing difierent typ es to cho ose difierent reactions: hence we might have some cartel typ es colluding and not revealing while others will prefer not to join the cartel; or we might have all typ es colluding, but only a subset of them revealing information when monitored, etc. Hence, the difierent efiects that we have identifled in the previous sections will b e combined in a richer way once the AA faces heterogenous typ es. F rom the previous analysis we already know that the incentive compatibility constraints for given p olicy parameters dep end on two v ariables of cartel’s typ e: ƒ ¡ ƒ and ƒ ¡ ƒ . Hence, M N D N Of course , l eniency rules which limi t the a ppli cabil ity of the flne re ductio n to only one flr m wi ll res ul t in a l arg er amo unt of money c oll ected thro ug h flnes. In a w orl d where non{disto rtionary transfers ar e no t av a ila bl e, this would b e an addi tional a dv anta ge of s uch rul es. 15 multiple typ es would require to deal with a biv ariate distribution, related to the gains from collusion and from deviation. T o maintain the analysis simple, we assume in this section Bertrand comp etition (with constant marginal costs ) in the non{co op erative equilibrium: hence ƒ =0 and ƒ = nƒ : N D M the gains from collusion are now p erfectly correlated to those from deviation, and we can consider a univ ariate distribution of typ es. Cartel typ es refer to the gains from collusion, due for example to difierent marginal cost levels, with ƒ 2 [ƒ ; ƒ ]; the AA do es not observe cartel typ es but M M knows their distribution g (ƒ ), and is not able to condition the p olicy chosen to some observ able that can make it contingent on a message. In other words, the AA sets a single combination of p olicy parameters taking into account that there exist many cartel typ es in the economy . Under the assumption of Bertrand comp etition the standard critical discount factor when an- titrust is absent, – =(ƒ ¡ ƒ )=(ƒ ¡ ƒ ), is (n ¡ 1)=n. W e can rewrite the relev ant lo ci as: D M D N ƒ (1 ¡ n + n– ) fi = =(– ¡ – ) =– CR ƒ n– which do es not dep end on cartel’s typ e, (1 ¡ – )n(– ¡ – )ƒ fi (p)= NC – [pF (1 ¡ –)+ƒ (p ¡ n(– ¡ – ))] and p ~ = (ƒ + F (1 ¡ – )) which are b oth increasing in ƒ . Moreover, fi is always ab ove fi at p = 1. Hence, when R< F M CR NC we can distinguish 5 regions which are represented in flgure 5. F igure 5 ab out he re fip In region A all typ es cho ose CNR and the corresp onding welfare is W = E (K ) whe re 1¡– +fi– E (K ) is the exp ected v alue of the gains from deterrence given the distribution of typ es g (ƒ ). In region B all typ es cho ose CR with W = E (K ) while in E all typ es abstain from collusion and 1¡– +fi– welfare is W = E (K ). In region C some typ es cho ose CNR and others CR: let ƒ be thetypewhose p ~ equals the p chosen by the AA in region C: all typ es lower than ƒ c oll ude and re ve al whil e t he cartels more profltable collude and don’t reveal. The exp ected welfare is therefore Z C Z ƒ ƒ fi M fip W = K (ƒ )g (ƒ )dƒ + K (ƒ )g (ƒ )dƒ C M M M M M M 1 ¡ – + fi– 1 ¡ – + fi– ƒ ƒ M M Analogously , in region D lower typ es abstain from collusion and higher typ es collude and don’t reveal, with the threshold typ e ƒ such that the actual p olicy combination in D lies on that typ e’s fi (p) NC curve. The exp ected welfare is then Z Z ƒ ƒ fip W = K (ƒ )g (ƒ )dƒ + K (ƒ )g (ƒ )dƒ D M M M M M M 1 ¡ – + fi– ƒ ƒ When R = F only regions A,D and E exist, deflned by the set of fi (p) curves which extend N C up to p =1. 16 The analysis of the optimal p olicy pro ceeds in three steps, which are develop ed analytically in the App endix. First, the iso{welfare curves in each of the flve regions A{E are derived; then, we check how the same welfare level is obtained passing (eventually) from one region to the neighb ouring one, distinguishing whether flne reductions are given or not; flnally , comparing the two cases, it is selected whether reduced flnes R allow to save enforcement costs, deflning a set of iso{welfare curves along which Leniency Programs are optimally used. The result of this analysis is shown in flgure 6.a: the lower b old curve is the iso{welfare (cost minimizing) curve setting R = 0, which passes through the regions A{C{B. The upp er b old curve passing in the D{C{B regions entains the use of reduced flnes only in a subset of the B and C regions. The p olicy combinations (R; fi; p) which minimize the cost of reaching the same exp ected welfare are summarized in a map of iso{welfare curves which are not convex: as b efore, we have to convexify them excluding from the set of p ossible equilibrium outcomes those p olicy combinations which b elong to the non{convex p ortions of the indifierence curves. Given the map of indifierence curves that minimize the cost of a given exp ected welfare, we exclude those p ortions which can never b e selected given our linear budget constraint .For the indifierence curves in the A region we obtain a subset of p oints E analogous to the one obtained CN R CR in the single typ e case already discussed. In region C we flnd a subset of p oints E in which some CN R typ es cho ose CR and higher typ es cho ose CNR. In region B we select only the b oundary to the left, CR NC which corresp onds to the E case when all typ es opt for CR. A subset of D, E is obtained CN R CN R where low typ e select NC and high typ es cho oase CNR, and flnally from region E we select the lower b ound. Once excluded the non{convex p ortions of the iso{welfare curves, the optimal p olicies for given budget constraint can b e established along the same lines of Prop osition 4’s pro of. W e summarize the results in the following Prop osition, which is respresented in flgure 6.b. Prop osition 5 Consider the optimal p olicy under asymmetric information given the budget c onstraint and the distribution of c artel typ es. † If the budget c onstraint p asses through re gion E, the optimal p olicy implements NC for al l typ es at a tangency p oint betwe en the budget c onstraint and the fi (p) curve of the highest typ e. N C NC † If the budget c onstraint p asses through re gion D and is tangent to an indifier enc e curve in E , CN R the optimal p olicy is at the tangency p oint with no flne re duction, and implements a CNR{NC outc ome ac c ording to the difierent typ es. † If the budget c onstraint p asses through re gion A and is tangent to an indifierenc e curve in E , CN R the optimal p olicy is at the tangency p oint and implements CNR for al l typ es. CR † If the budget c onstraint p asses thr ough C and is tangent to an indifierenc e curve in E ,that CN R is the optimal p olicy and implements a CNR-CR outc ome. † In al l the other c ases the optimal p olicy implements CR for al l typ es setting p e qual to the p ~ of the highest typ e along the budget c onstraint. An y c onv ex budg et s et, a s tha t o btai ne d under the as sumptio n of decr easi ng re turns to enforce men t, w o ul d al low a si mila r exerci se. 17 Figures 6.a and 6.b ab out here W e can give an explanation of the result ab ove considering the sequence of optimal p olicies when the budget constraint b ecomes steep er and steep er as a result of an increase in the cost of indep endent prosecution (higher w ). F or low v alues of w the p olicy implements full deterrence ex{ante for all p p typ es. As the budget constraint rotates toward the origin we initially move to a CNR{NC mixed outcome with no flne reduction, in which the more profltable cartels are not deterred. Granting flne discounts in this case would shift low typ es from NC to CR: the pro{collusive efiect of Leniency Programs would dominate reducing welfare. However, when the fraction of low typ es which cho ose NC shrinks further, reduced flnes are intro duced, inducing all typ es to collude and reveal. In this case the improvement in prosecution allowed by reduced flnes b ecomes predominant. A further increase CR in w moves the equilibrium outcome in the E region with an increasing p ortion of high typ es CN R that cho ose CNR while low typ es collude and reveal. The implicit cost of the Leniency Programs, which forces the AA to commit resources to indep endent prosecution to make it a credible threat, b ecomes heavier and heavier as the resources left to op en inquiries decrease and as the fraction of typ es which are induced to reveal shrinks. In the end we move to the E region, abandoning the CN R Leniency Program. Hence, the optimal p olicy is determined, in a sense, by the relative imp ortance of the pro{welfare efiect of Leniency Program, that allows to obtain more efiective ex{p ost desistence, and the welfare decreasing efiects of reduced flnes: the incentive to collude (and reveal) instead of abstaining from collusion, and the need to sink resources to make indep endent prosecution credible, which reduces the probability of op ening an inquiry and of obtaining ex{p ost desistence. 5 Conclusions In this pap er we have analyzed the efiects of Leniency Programs on the incentives of flrms to collude and to reveal information that helps the Antitrust Authority to prove illegal b ehaviour. The b enchmark regime gives to any flrm a reduction in flnes even if revelation o ccurs after an investigation is op ened. W e show that reducing the exp ected flnes may induce a pro{collusive reaction: combinations of p olicy parameters which, without Leniency Programs, would prevent collusion, may induce flrms to collude (and reveal if monitored) when flne reductions are given. Hence, if the resources av ailable to the AA are su–cient to prevent collusion using full flnes, Leniency Programs should not b e used. However, when the AA has limited resources, Leniency Programs may b e optimal in a second b est p ersp ective. Fine reductions, inducing flrms to reveal information once an investigation is op ened, increase the probability of ex{p ost desistence and the exp ected welfare gains. The optimal scheme requires maximum flne reductions and a shift of resources from prosecution to monitoring. A flxed amount of resources, however, must b e committed in any case to make indep endent prosecution a credible threat, since no flrm would reveal if it exp ects that the AA is unable to prove them guilty . When indep endent prosecution is very costly , to o few resources are left to general monitoring, which in the end determines the efiectiveness of Leniency Programs. In this case it may b ecome more convenient to shift back to a full flnes regime with a more favourable mix of p olicy parameters. W e have then compared our b enchmark regime with alternative sets of rules: the flrst allows to give flne reductions only to flrms which co op erate with the Antitrust Authority b efore an inquiry 18 is op ened, as initially established in the US p olicy in 1978, and similar to the approach followed by the EC Notice on the non-imp osition of flnes, and we proved this regime to b e inferior with resp ect to our b enchmark case. W e have then considered other rules which restrict the set of the flrms that can b eneflt from a Leniency Program. W e showed that by granting a flne reduction only to the flrst flrm which co op erates with the AA the p erverse pro{collusive efiect of the Leniency Program would b e reduced without softening the incentives to reveal information. Better still, the AA might target a sp eciflc flrm and allow only this one to b eneflt from the reduction. The intuition for this result, which makes the Leniency Program even more efiective, lies in the asymmetry that the p olicy intro duces among otherwise identical flrms, b etween the entitled flrm and the excluded ones: the latter would more often prefer to abstain from collusion rather than join a cartel together with a likely cheater. Finally , the case of multiple cartel typ es has b een considered: the AA is assumed to b e unable, for informational or institutional reasons, to implement Leniency Programs contingent on cartel’s typ e, and therefore has to set general rules. F or instance, the AA cannot shap e the p olicy to the conditions of each sp eciflc industry , but has to cho ose a general rule of b ehaviour, obtaining difierent efiects in difierent industries. Then, according to the p osition of the budget constraint in the set of p olicy combinations, we characterized the optimal p olicy: it turns out that the p olicy parameters and the regime of full or reduced flnes are chosen according to the relative weight of the three efiects describ ed ab ove, where the weights dep end on the share of typ es which cho ose the difierent equilibrium outcomes (no collusion; collusion; collusion and revelation). W e b elieve that, despite the simple setting, our pap er sheds some light on the desirable features of leniency programs, and suggests some changes in the EC leniency p olicy . First of all, if it is optimal to use a leniency program (as in the realistic case where the antitrust agency has limited resources), then the program should b e as generous and certain as p ossible with the flrms which provide fresh evidence that establishes the existence of a cartel. In contrast, the EC p olicy of keeping some degree of discretionality instead of granting automatic and total reduction of flnes even to those flrms which fulfll all the (strict) conditions laid down in the EC Notice undermines the success of the leniency program, as it does not give certainty to the prosp ective co op erating flrm and reduces the incentive to break the cartel. Likewise, some of the conditions required by the EC p olicy are to o strict. F or instance, a flrm must \maintain continuous and complete co{op eration throughout the investigation" to b e entitled to have a very substantial reduction (more than 75%) of the flne. This has led the Commission to give only a 50% reduction to a flrm, T ate & Lyle, which had sp ontaneously brought conclusive evidence of a cartel to the attention of the Commission (at a time when the Commission did not even susp ect the existence of an agreement), but had later (partially) contested some of the allegations made by the Commission . The strict wording and application of the Notice will reduce the incentive of the flrms to reveal information . F urthermore, our analysis indicates that a leniency program should b e equally applicable to information disclosed b efore and after an investigation has started, whereas the EC p olicy do es not Thi s is the ca se \Br itish Suga r", EC Deci si o n of 14 Octob er 199 8, publi shed i n the O–cia l Journal o f the EC, L76, 22 March 1 99 9. Hornsby a nd Hunter (19 97 ) als o p oi nt o ut that the flrms do not have enough incentives to co op era te under the EC p ol icy . Part of the pro bl em i s a lso due to the fact that the No ti ce c anno t pr ovi de immuni ty from c ivi l pro ceedings. Admi ssio n of a n infri ng ement le ads to a fo rmal Commis sio n De cisi on o n which a n acti on for da mage s ca n b e built, without the plai nti fi havi ng to prov e the infring ement aga in. This pro bl em do es not exi st i n the US, where the co o p erating flrms ca n reso rt to a co ns ent dec ree. 19 create enough incentives for p ost{investigation disclosure of information. It gives only 50{75% reduc- tion of the flnes for co op eration after an investigation has b een undertaken already but only if such an investigation has failed to provide su–cient material for initiating a pro cedure leading to a decision. The US exp erience (where after the 1993 p olicy revision a corp oration is granted leniency after an investigation has b egun provided that \the Division, at the time the corp oration comes in, does not yet have evidence against the company that is likely to result in a sustainable conviction" | p oint B.2.) clearly shows that extension of the leniency program to p ost{investigation amnesty (along with the automatic granting of the amnesty) is a crucial ingredient for success: \...under the old p olicy on average only one corp oration p er year applied for amnesty ," (Spratling (1998, page 2) whereas under the revised p olicy , \Amnesty applications over the past year have b een coming in at the rate of approximately two p er month" (Spratling (1999, page 2). So far, the leniency program of the EC has b een applied to a very reduced numb er of cases, since its intro duction in the end of 1996. There was no case in 1997 and only four in 1998 .We b elieve that granting higher and automatic reductions of flnes and extending the leniency program to after{investigation co op eration would greatly increase the success of this p olicy . References [1] Antitrust Division (1994), Annual Rep ort for Fisc al Y e ar 1994. [2] Beb chuk L. (1984), Litigation and Settlement under Imp erfect Information, Rand Journal of Ec onomics, 15, 404{413. [3] Bingman A., Spratling G., (1995) Criminal Antitrust Enforcement, mimeo. [4] Europ ean Union (1996), Notice on the Non{Imp osition or Reduction of Fines in Cartel Cases, O–cial Journal, v.207, p.4. [5] Europ ean Union (1999), Comp etition Policy Newsletter, No.1, F ebruary . [6] F urse M., (1995), Article 15(2) of Regulation 17: Fines nad the Commission’s Discretion, Eur o- p e an Comp etition L aw Review, p.110. [7] Grossman G., Katz M. (1983), Plea{Bargaining and So cial W elfare, American Economic Review, 7, 749{757. [8] Guerrin M.(1999), Priv ate communication. Electronic message of 5 March 1999. Infor matio n provided by an EC o –cia l, G uerri n (1 99 9). Of these, three rega rded instances of mi no r co op erati on (flrms were given disco unts for not having contested the Commi ssi on’s all ega tions or fo r providing a dditi onal evidenc e which help ed establi shing the facts ). Thes e cas es are \ Al loy surcha rge" , E C Decis ion of 21 Janua ry 1 998 ; \P re-i ns ul ated pip es" , EC Deci sio n o f 21 Octo b er 1 99 8; \ Greek F erri es" , EC Deci sio n o f 9 Decemb er 19 98. The fourth c ase was the \Britis h Sugar" cas e rep orted in the previo us fo otnote, whi ch mi ght b e a di sco ura ging prece dent fo r flrms consideri ng co op erati on with the Co mp etitio n Co mmiss ion. According to Guerri n, i n so me furthe r hal f a dozen current ca ses the Leniency Notic e has b een invoked. No further detail s were gi ven for rea sons of co nfldenti ali ty . 20 [9] Hornsby S., Hunter, J. (1997), New incentives for \whistle{blowing": will the E.C. Commission’s Notice b ear fruit?, Europ ean Comp etition Law Review, 1, 38{41. [10] Kobayashi B. (1992), Deterrents with Multiple Defendants: an Explanation for \Unfair Plea Bargains", Rand Journal of Ec onomics, 22, 507{517. [11] Marshall R., Muerer M., Richard J. (1994), Litigation, Settlement and Collusion, Quarterly Journal of Ec onomics, 1, 211{239. [12] Nalebufi B. (1987), Credible Pre{Tial Negotiation, Rand Journal of Ec onomics, 18, 198{210. [13] Reinganum J. (1988) Plea{Bargaining and Prosecutorial Discretion, Americ an Ec onomic Review, 78, 713{728. [14] Reinganum J., Wilde L. (1987), Settlement, Litigation and the Allo cation of Litigation Costs, Rand Journal of Ec onomics, 17, 557{566. [15] Schweizer U. (1989), Litigation and Settlement under Two{Sided Incomplete Information, Review of Economic Studies, 56, 163{178. [16] Shavell S. (1989), Sharing Information Prior to Settlement or Litigation, Rand Journal of Ec o- nomics, 20, 183{195. [17] Spratling G.R. (1998), The corp orate leniency p olicy: answers to recurring questions, sp eech of the Deputy Assistant Attorney General, presented at the Bar Asso ciation of the District of Columbi a, F ebruary 16, 1999. [18] Spratling G.R. (1999), Making companies an ofier they shouldn’t refuse, sp eech of the Deputy Assistant Attorney General, presented at the ABA Antitrust Section 1999 Spring Meeting, April 1, 1998. [19] V enit J. (1996), EU Comp etition Law | Enforcement and Compliance: An Overview, Antitrust L aw Journal, p.87. Appendix Pro of of Lemma 1 If a flrm reveals, it ge ts a payofi of ƒ =(1 ¡ – ) ¡ R indep e ndentl y of the action chosen by the other flrms. If a flrm do es not reveal any information but at least one flrm do es, then the former flrm receives a payofi of ƒ =(1 ¡ – ) ¡ F . Hence, it is always (weakly) b etter to reveal if the other flrms are exp ected to reveal, which establishes the existence of the \revelation" equilibrium. Finally , if no flrm reveals any information, each flrm receives an exp ected payofi. ƒ ƒ N M p( ¡ F )+ (1 ¡ p) : (15) 1 ¡ – 1 ¡ – 21 If a flrm exp ects the others not to reveal, the b est reply is trivially not to reveal if pF < R.If pF ‚ R, when the other flrms don’t reveal, a flrm prefers not to reveal as well if the payofi ab ove is higher than ƒ =(1 ¡ – ) ¡ F , which simplifles to – ‚ – (p; F ; R). Hence, in this case a \no revelation" equilibrium exists. Moreover, the same inequality implies that the \no revelation" equilibrium gives higher payofis to all flrms than the \revelation" equilibrium. Pro of of Prop osition 2 W e consider the decision to collude or deviate in b oth cases, when flrm will decide to reveal if inves- tigated, and when they will prefer not to co op erate with the AA. † Case 1: –< – . In this case flrms reveal if an investigation is op ened by the AA. Deflne ƒ as the exp ected proflt immediately b efore an investigation is op ened. It is easy to see that: ƒ = fi( ¡ R)+ (1 ¡ fi)(ƒ + – ƒ ) R M R 1 ¡ – from which we obtain: (1 ¡ fi)ƒ + fi( ¡ R) 1¡– ƒ = 1 ¡ – (1 ¡ fi) If a flrm decides to set the collusive price, then its exp ected discounted payofi will b e: ƒ + –fi( ¡ R) 1¡– V =ƒ + – ƒ = CR M R 1 ¡ – (1 ¡ fi) If instead a flrm decides to deviate from the collusive strategy , then its payofi is given by: – ƒ V =ƒ + D D 1 ¡ – Collusion can arise if V ‚ V , that is if the following condition is satisfled: CR D ƒ ¡ ƒ D M – ‚ · – (fi; R): (16) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N † Case 2: – ‚ – . In this case, flrms anticipate that even if an investigation is started, no flrm will reveal any information. Collusive outcome will b e obtained unless the AA can prove the flrms guilty of collusion. W rite the exp ected proflt immediately b efore knowing if an investigation is op ened as: ƒ ƒ N M ƒ = fi[p( ¡ F )+ (1 ¡ p)( )]+(1 ¡ fi)(ƒ + – ƒ ) NR M NR 1 ¡ – 1 ¡ – W e can then obtain: ƒ ƒ N M fi[p( ¡ F )+ (1 ¡ p)( )] + (1 ¡ fi)ƒ 1¡– 1¡– ƒ = NR 1 ¡ – (1 ¡ fi) If a flrm follows the collusive strategy its exp ected discounted payofi is given by: 22 –fi(1¡p) ƒ (1 + )+ –fip( ¡ F ) 1¡– 1¡– V =ƒ + – ƒ = CN R M NR 1 ¡ – (1 ¡ fi) As b efore, a flrm which deviates obtains a payofi: – ƒ V =ƒ + D D 1 ¡ – The inequality V ‚ V implicitly deflnes the lo cus of p oints – = – (fi; p; F ). CN R D NC NC Pro of of Prop osition 4 W e pro ceed in two steps: flrst we show, for each given outcome NC, CR, CNR, which is the asso ciated optimal p olicy; second, we show the conditions under which a particular outcome is b etter than the others. If a NC outcome is implemented, we can have two cases: either the budget constraint is ab ove t he l ower b oundary of the A region or it is tangent: in the latter case the tangency p oint N C with the fi curve is trivially the optimal solution; if the budget constraint is ab ove that curve, the NC tangency p oint can still b e suggested under a cost saving argument. In this case we set R = F since granting flne discounts would shrink the A region. If a CR outcome is implemented, the welfare NC gain dep ends only on fi, which therefore must b e maximized: we can therefore set R = 0, shifting to the left the p ~ threshold, and setting p =~ p; with p at its lowest level in the A region we can set CR fi = B=w ¡ (w =w )~ p along the budget constraint. Finally if a CNR outcome is chosen, a tangency fi p fi p oint b etween the budget constraint and the indifierence curve in the A region must b e chosen. CN R Consider now the choice among the three outcomes: since W is always dominant for any N C set of p olicy parameters, if the budget constraint is not b elow the fi (p) curve, NC is the optimal NC outcome implemented. The choice b etween a CR and a CNR outcome is more complex, since b oth W and W dep end on the asso ciated p olicy parameters, which, in turn, are difierent at the CN R CR optimal p oints in the two regimes. Supp ose the tangency p oint in the A region b elongs to the CN R subset E : from the deflnition of E , even if the budget constraint in its lower p ortion reaches CN R CN R the A region, it passes through indifierence curves lower than the initial one: hence, picking the CR tangency p oint in the E region and implementing a CNR outcome is the optimal p olicy . On the CN R contrary , if the tangency p oint is in A but not in E , the budget constraint reaches the A CN R CN R CR at a higher indifierence curve, and a CR outcome is optimal. The iso{welfare curves with heterogeneous cartel typ es In the following three Lemmas we identify the iso{welfare curves when the AA faces heterogeneous cartels. Lemma 6 The iso{welfare curves in e ach of the flve re gions have the fol lowing p attern: † in E al l the p olicy c ombination give the same welfare; † in A and D they r eplic ate the shap e of the fi (p) curves; N C † in B they are horizontal; 23 † in C t hey ar e de cr e asing; Pr o of: Since W do es not dep end on the p olicy parameters, all the region corresp ond to the same exp ected welfare. In region A all typ es cho ose CNR. F rom our analysis of the single typ e case we already know that the iso{welfare curves when no typ e colludes have a shap e similar to the fi NC curves (one for each typ e) and in the limit overlap with those. Hence, in region A the indifierence curves replicate the fi curves shap e. In region D high typ es cho ose CNR and lower typ es cho ose NC NC: as long as we move along the fi curve of typ e ƒ , the threshold typ e do es not change and the NC flrst term in W i s unchange d as we ll; moreover, we know that moving along a fi curve we keep the D N C exp ected welfare for typ es cho osing CNR constant. W e conclude that the indifierence curves in region D corresp ond to the fi curves through it. In region B all typ es cho ose CR and the exp ected welfare NC dep ends only on fi, i.e. we have at iso{welfare curves. Finally , in the C region high typ es select CNR and low typ es CR: since W increases when fi is higher (more frequent revelation) as well as when p increases (more efiective prosecution and more typ es induced to reveal), the iso{welfare curve in the C region must b e decreasing. 2 Notice that when no Leniency Program is used, only the regions A, D and E exist, and the result ab ove states that all the curves in A (or D) never pass through another region. Hence, the three relev ant sets of indifierence curves are completely deflned. When R< F all the flve regions A{E exist; the Lemma ab ove deflnes the iso{welfare curves in each region, but now the iso{welfare curves in A (D) eventually continue through region C and B. Hence, we have to carefully check how the iso{welfare curves b ehave moving from one region to the other. Lemma 7 Consider the c ase R<F . The iso{welfare curves p assing through the re gions A{C{B are c ontinous and kinke d at the boundaries of the A and B re gions. The iso{welfar e curves p assing thr ough the re gion D{C{B disc ountinously shift to the right p assing fr om D to C. Pro of: W e start by identifying the indifierence curves that pass through the A{C{B regions. W e already know, b orrowing from the analysis of the single typ e case, that the iso{welfare curve jumps down from A to B, when all typ es cho ose CNR and then CR: however, from the deflnitions of the exp ected welfare we can notice that W tends to W or W as the threshold typ e ƒ tends to ƒ or C A B M ƒ . Hence, the indifierence curves are now continuous; it is easy to check also that they are kinked at the b oundaries of the A and B regions, with the indifierence curve steep er in C than in the other two regions . Consider next the indifierence curves passing through the D{C{B regions: we already established that in D the curves replicate the fi curves shap e, with some typ es cho osing CNR and others NC; NC once moving into the C regions, some typ es still select CNR while others CR. Since the welfare asso ciated to NC is higher than that when CR o ccurs, it must b e that, moving from region D to region C along a iso{welfare curve, less typ es cho ose CNR. That requires a discontinuous jump to the right of the iso{welfare curve once entering in the C region. 2 The concavi ty o r conv e xity of the i ndifiere nce curve in C cannot b e state d i n g eneral, since it dep ends on the distri bution of t yp es g (ƒ ). In what foll ows we consider the case o f concave indi fierence curves, while the extensi on to the co n vex ca se is left to the re ader. 24 Figure 6.a shows the two cases of indifierence curves, one through A{C{B and the other through D{C{B. In the two Lemmas ab ove we have completely characterized the iso{welfare curves when a Leniency Program is intro duced and when it is not. Our next step is to verify when it is convenient to ofier reduced flnes in order to reach a certain exp ected welfare. This exercise correp onds to comparing the iso{welfare curves in the two cases, selecting in the difierent regions the lower one. Lemma 8 When the iso{welfare curve with R =0 p asses thr ough the A{C{B r e gions,it is always optimal to use the leniency Pro gr ams. When the iso{welfare curve with R =0 lies in the D{C{B re gion, the L eniency Pr o grams ar e optimal only in a subset of the C and B re gions. Pro of: Si nc e R = 0 is the more efiective way of inducing CR, we compare the case R = F and R = 0, selecting the lower of the two iso{welfare curves. Since in A and D the iso{welfare curves are the same in b oth regimes, our problem amounts to selecting the lower curve in regions C and B. This can b e done by distinguishing the case in which the indifierence curve with flne reduction passes through the A{C{B region and that in which it lies in the D{C{B areas. Comparing the full and reduced flnes indifierence curves is immediate for the A{C{B case: in the A region they overlap while in the C and B region the iso{welfare curve is lower when R = 0, as shown in flgure 6.a. Hence, the iso{welfare curve through A{C{B is that identifled when the Leniency Program is used. More complex is the comparison of the indifierence curves with and without flne reductions when the former passes through the D{C{B region. In this case, in fact, the iso{welfare curve with flne reductions jumps to the right entering the C region, while with no Leniency Program the indifierence curve, which is the same as b efore in the D area, go es on smo othly in the C region . Hence, entering the C region from the top, the lower indifierence curve is initially the one asso ciated with no flne reduction. It may happ en, as shown in flgure 6.a, that continuing along it, the indifierence curve with flne reductions b ecomes the lower one for a while. Finally , moving further to the right, the indifierence curve with full flnes lies again b elow that with flne reductions. F or higher levels of the exp ected welfare, the indifierence curve with full flnes always dominates that with reduced flnes. Hence, when we consider the indifierence curves for increasing v alue of the exp ected welfare, as long as we are in the A{C{B region we use Leniency Programs, while entering the D{C{B region we adopt reduced flnes only with a subset of p olicy parameters (fi; p), as shown in flgure 6.a. 2 Strictly s p e aking, with no Leniency Prog ra m no C regi on exis ts ; hence we refer to the C reg ion a s thos e p ol icy co m binati ons deflned i n cas e o f flne reduc ti ons. 25 t=0 t=1 t=2 AA F,R a, p f1 D C AA V P D M I a 1-a NI AA f1 P R NR I a 1-a NI f2 R NR R NR f1 P /(1-d)-R P /(1-d)-F AA R NR N N P /(1-d)-R G p 1-p NG P /(1-d)-F P /(1-d) f2 N M R NR R NR P /(1-d)-R P /(1-d)-R AA N N P /(1-d)-R G NG p 1-p P /(1-d)-F P /(1-d) N M Figure 1: The game tree (D: deviation; C: collusion; I: investigation; NI: no investigation; R: reveal; NR: not reveal; G: guilty; NG: not guilty)  E2 E Z 3Z Z 3Z f  6}hi 2@  W4T*i4i?|@M*i @**LU@|L?t  E E2 6}hi 2M  W4T*i4i?|@M*i @**LU@|L?t  f  6}hi ,^*Mh4 TL*U) UL4M?@|L?t  - B f  6}hi e  *|ih?@|i wi?i?U) h*it @?_ 4T*i4i?|@M*i @**LU@|L?t  ( . f  6}hi D  *|T*i |)Tit @?_ 4T*i4i?|@M*i @**LU@|L?t  f  6}hi S@  WtLi*u@hi Uhit | 4*|T*i |)Tit  f  6}hi SM  ,^*Mh4 TL*U) UL4M?@|L?t | 4*|T*i |)Tit http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SSRN Electronic Journal Unpaywall

Leniency Programs and Cartel Prosecution

SSRN Electronic JournalJan 1, 1999

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1556-5068
DOI
10.2139/ssrn.165688
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Abstract

,N+, NWV,+5WAv W5AWANA, #,+A,A 6 ,W5 ,NW `Lh!?} @Tih , L bb%2 wi?i?U) hL}h@4t @?_ @h|i* hLtiU|L? Btt6N N||B @?_ Wj,j N,N #W 6W,5wc 5 #,W E6W ** h}|t hitihi_ L T@h| Lu |t T@Tih 4@) Mi hiThL_Ui_ ? @?) uLh4 |L| Tih4ttL? Lu |i @|Lh U bbb  L||@ @?_  L*L h?|i_ ? W|@*) ? a*) bbb ,hLTi@? N?iht|) W?t|||i @_@ 6itL*@?@ WDffS 5@? #L4i?UL E6W W|@*) Leniency Programs and Cartel Prosecution Massimo Motta Michele Polo European University Institute, Florence Bocconi University and IGIER, Milan Universitat Pompeu Fabra, Barcelona June 7, 1999 Abstr act W e st udy the enforcement of comp etition p olicy against collusion und er Leniency P rogr am s, which give r ed uced flnes to flrm s revealing in for mation to t he Ant itru st Aut hor ity . S uch programs give flrms an incent ive to break collu sion, but may also have a pro{collusive efiect, since t hey decr ease the exp ect ed cost of m isb ehaviou r. W e analyze the optim al p olicy un der alter nati ve r ules and with homogeneous an d h et erogeneous cartels, obtaining a ranking of the difi er ent schemes and showing when t he u se of r educed flnes may imp rove antitr ust enforcement. W e b eneflted from di scussi ons with Luis Cabral, F ederico G hez zi, Patri ck Rey , Thomas V o n Ung ern{ Ste rnb erg and semi na r parti cipants a t the Unive rsity of Sal erno and the Europ ea n Universi ty Institute (Fi eso le). Thei r co mments a re gra tefull y ac knowle dg ed. 1 Introduction The enforcement of comp etition p olicy against collusion and price flxing agreements is one of the main flelds of antitrust intervention. Recent developments show that the attention devoted by antitrust authorities to collusive agreements has not diminished over time. Recently , the DGIV, the Directorate{ General of the Europ ean Union in charge of comp etition p olicy , has established a sp ecial investigation unit against cartels , and a similar pattern can b e found in the US, where the Antitrust Division of the Department of Justice has reallo cated and improved the resources of the Criminal section in charge for cartel prosecution . In the design of the p olicy we flnd to day richer and more complex mechanisms than those based simply on an increase in flnes. Since 1978 the US Antitrust Division of the Department of Justice has allowed for the p ossibility of avoiding criminal sanctions if sp eciflc conditions o ccurred. In 1993 this p olicy has b een redesigned in the Corp orate L eniency Policy, which establishes that criminal sanctions can b e avoided in two cases: either if a colluding flrm reveals information b efore an investigation is op ened, as it was in the previous regime, or if the Division has not yet b een able to prove collusion when a flrm decides to co op erate . The new Leniency Policy has shown in the flrst years of application a signiflcant success in terms of the numb er of cases that the Division has b een able to op en and successfully conclude. The current EU system draws from the US exp erience. In order to reach a more efiective deterrence of collusive practices, the DGIV has initially fo cused its enforcement p olicy on a sharp increase in flnes: the average flne given to flrms involved in collusion cases, up to the mid Eighties has remained b elow 500.000 ECU while in the last decade it has reached an average of around 1.500.000 ECU . However, if the flrms anticipate a low probability of having collusive practices discovered (and proved), flnes alone will b e insu–cient to prevent flrms from establishing cartels. Although it is hard to quantify such exp ected probabilities, there seems to b e a wide p erception that the deterrence efiects of the flnes has b een relatively p o or, and that v arious typ es of collusive practices are still widespread. This has pushed the Europ ean Union to intro duce a new regime in which reduced flnes can b e given to flrms which co op erate with the antitrust authority by providing evidence of a collusive agreement in which they have b een involved. A 75{100% reduction in flnes can be givenifflrms reveal information b efore an inquiry is op ened, while a lower reduction (50{75%) can b e granted if co op eration o ccurs after an investigation has started, but that investigation has failed to provide su–cient grounds for initiating a pro cedure leading to a decision. A 10{50% reduction in flnes can b e given for partial co op eration, such as providing additional evidence or not contesting the facts on which the Commission bases its allegations. Moreover, only the flrst flrm which co op erates can obtain a reduction, provided that it is not the promoter and ma jor partner of the cartel. It is to o early to ev aluate the efiects of this new p olicy , although the US exp erience suggests that enforcement against cartels might b ecome more efiective. See V enit (1 99 6), p.92 , and Europ ea n Unio n (19 99 , p. 22). See Bi ng man a nd Spratl ing (1 99 5). Some additio na l restricti ons o n the flrms en ti tl ed to b eneflt fro m this regi me a re in tro duced, as the fact that only the flrst can b e gi v en a flne reducti on, and tha t i t must b e a junior partner i n the ca rtel. See F urs e (1 995 ), p. 114 . European Uni on (1 996 ). Notic e that while in the US the regime a ppli es to cri minal sa ncti ons (whi ch include b o th flnes and inca rcerati on), in the E U reducti ons are refe rred only to mo ne tary flne s. Crimina l s anctio ns do no t exis t under EU co mp etitio n law. 1 In this pap er we want to investigate the difierent efiects that the intro duction of a Leniency Program can have on b oth flrms’ b ehaviour and deterrence. Our work is related to other pap ers on the optimal enforcement of law, sp eciflcally those on pre{trial negotiation and settlement and on plea{bargaining , in which these alternative judicial pro cedures have b een studied with a general reference to the US judicial system, although not explicitly to antitrust law. There are however several imp ortant difierences b etween our work and the existing literature. The pap ers on pre{trial negotiation have considered mainly the prop erties of these pro cedures in saving trial costs preventing wasteful litigation. In the plea bargaining literature the enforcer acts more explicitly on b ehalf of taxpayers, balancing the goal of condemning the guilty agents and not condemning the inno cent ones with the minimization of resources devoted to enforcement. In b oth cases, the issue of deterrence is not really addressed: agents have (p ossibly) already committed a crime, and in most pap ers, whether the agent is inno cent or guilty and how strong is the evidence against him (agent’s typ e) is exogenous in the mo del, and it is not explained in terms of incentives to commit a crime. The efiects of the legal pro cedures on preventing the crime or making it to cease are instead at the center of our analysis. In our pap er we are mainly concerned with the deterrence and desistence prop erties of negotia- tions b etween the Antitrust Authority and priv ate flrms. The enforcer is motiv ated by the maximiza- tion of so cial welfare and aims at minimizing the o ccurrence of collusion among flrms by committing on a certain set of p olicy parameters . In order to fo cus on deterrence, in our setting we exclude other ingredients already studied in the literature. First of all we do not consider (v ariable) litigation costs on either party , a central issue in the pre{trial negotiation literature. The enforcer’s budget is set at the b eginning of the game and enforcement costs are sunk, i.e. they are already allo cated among the difierent tasks of the organization, as general monitoring or prosecution. Secondly , we do not consider the p ossibility of wrong sentences, analyzed in the plea{bargaining pap ers: at the end of an investigation either a guilty flrm is condemned or no evidence is reached. In this setting we consider several issues. First of all we analyze the reaction of flrms to difierent p olicy regimes, i.e. on the incentive to collude and on the decision to reveal or not information to the Antitrust Authority . A p erverse efiect can arise under this resp ect: since a Leniency Program allows flrms to pay reduced flnes, it may have ex-ante a pro{collusive efiect, decreasing the exp ected cost of anticomp etitive b ehaviour. But we show that, if the Antitrust Authority has limited resources, and is therefore unable to prevent collusion ex{ante, the use of Leniency Programs can improve the efiectiveness of the p olicy , by sharply increasing the probability of interrupting collusive practices. Hence, in a second b est p ersp ective, flne reductions may b e desirable b ecause they allow to b etter implement ex{p ost desistence from collusion. There is however a third comp onent that op erates in equilibrium: in order to induce flrms to reveal, a Leniency Program has to commit resources to guarantee a su–ciently high probability of indep endent prosecution. This is the implicit cost of a reduced flnes regime, since those resources are subtracted from the general monitoring activity , which determines the frequency of \revelations" and successful inquiries. As the resources committed to prosecution b ecome to o costly , a Leniency The US Leniency Prog ram i nvolves b o th reductio ns of flnes and the el iminati on of the threa t of incarce ratio n. In this pa p er we fo c us o n reduce d monetary flnes. He nce , we use the te rm Leniency P rogr ams in a broa d se ns e. Beb chuk (19 84), Nale bufi (1 987 ), Schwei zer (1 98 9), Shavell (19 89 ). Gr oss man a nd Ka tz (19 83 ), Reing anum (198 8). Othe r pap ers that are rela ted to our own are Ko baya shi (1 99 2) a nd Ma rshall , Muerer and Ri cha rd (19 94 ). 2 Program loses its app eal, and a full flnes regime may b ecome more convenient again. The conditions under which these results hold will b e identifled in b oth a homogeneous and a heterogeneous cartel setting. The efiects and desirability of alternative leniency rules will also b e studied. The pap er is organized as follows. In section 2 we set up the basic mo del, in which every flrm which decides to co op erate with the Antitrust Authority is given a flne reduction. In section 3 we consider alternative Leniency Programs, in which flne reductions can b e granted only if co op eration o ccurs b efore an investigation is op ened, or in which only the flrst comer, or a sp eciflc flrm, is entitled to a reduced flne. Finally , in section 4 we extend the basic mo del to the heterogeneous cartels case. Section 5 concludes the pap er. 2TheModel Throughout the pap er, we assume that the Antitrust Authority (AA from now on) aims at maximizing a utilitarian so cial welfare function and is able to commit to a certain set of p olicy parameters ,which consist of full and reduced monetary flnes and probabilities of enforcement. In the basic mo del of this section we consider a regime in which al l flrms which co op erate in the investigation even aft er this has b een op ened, and which simultaneously provide useful evidence to prove collusion , can b ene flt from a reduction in flnes. In the following sections we shall consider alternative rules and compare them with this b enchmark case. The AA is (exogenously) endowed with a p er{p erio d budget B : in line with the literature, we assume that setting the flnes at any level is not costly , while increasing the probability of enforcement requires resources. More precisely , we assume that the maximum flne that flrms can receive if found guilty of collusion is exogenously given by law and equal to F , a flxed amount of money: then, b eing costless, it is always optimal to set the full flne at this maximum level. However, the AA can commit to a Leniency Program which allows for reduced flnes R • F to flrms which reveal information useful to prove the existence of collusion. Indirectly , that is via the allocation of its given resources among difierent tasks, the AA determines the probability fi of op ening an investigation and the probability p of proving flrms guilty . The former refers to the preliminary activities (general monitoring) necessary to op en an investigation such as collecting information ab out the flrms in the industry , interviewing flrms, suppliers and customers, collecting data from the difierent sources; the latter (prosecution) involves collecting further more fo cused information on the case, ordering surprise \raids" in the flrms’ headquarters, pro cessing the information collected and preparing the case against the flrms according to the existing laws. The AA, allo cating resources to these two groups of tasks can obtain a combinations of these probabilities according to their sp eciflc pro duction functions . The budget Thi s i s in li ne with actual exp erience, in which li ttl e dis cretio n is left by the law to the Autho rity as to the co nditio ns under which reductio ns ca n b e given, and the ir amoun t. Thro ug hout the pap er, w e ass ume tha t informati on g iv en b y a si ng le flrm is enough to prove that a ll the flrms which hav e ta k en part i n the co llusi on are guilty . Thi s mi gh t b e in terpreted a s the cas e where e ach flr m ha s a ccess to the minute s of the meetings whi ch take pl ace a mong al l the co lluding flrms, o r ha s copie s of l ette rs, faxes o r e {mai l mess ages which all the flrms hav e used to co ordinate on the col lusive o utc ome. Since an imp ortant co mp onen t in the w orking of ca rte ls i s the co ordinati on of moves a mong parti cipants, the a ccess of each partner to so me info rmatio n rega rdi ng the others see ms quite real istic . More prec isel y , le t the AA budget c onstraint b e B = w (l + l ); where B is the tota l budg et av ai lable to the Autho rity; fi p l the numb er o f hours all o ca ted to ge nera l mo ni toring and l tho se dev o ted to prose cuti on, w the w ag e rate. In turn, fi p the pro babili te s are determi ne d g iv e n the res ources a ccording to the pro ductio n functi ons fi = k l , and p = k l , with fi fi p 3 constraint is then: B = w fi + w p (1) fi p where w and w are the (constant) unit cost of monitoring and prosecution. W e assume that flrms fi p know the probabilities fi and p chosen by the AA and its budget constraint. The AA ob jective function is a standard utilitarian welfare function, i.e. the sum of pro ducers and consumers surplus. Fines, whether full or reduced, are pure transfers, i.e. they go to the general government budget and are redistributed to consumers without distortions, and cannot b e used by the AA to increase its budget. The agency problem can therefore b e describ ed as cho osing the incentive sche me (R; fi; p) in order to inuence flrms’ b ehaviour and maximize so cial welfare. The incentive compatibility constraints will b e derived from the analysis of the subgame p erfect equilibria in the sup ergame played by flrms once the p olicy parameters are set. After observing the p olicy parameters chosen by the AA, n identical flrms decide whether to collude or not, by correctly taking into account the probabilities (fi; p) and by knowing whether a Leniency Program R is in place or not. W e follow the usual sup ergame literature and consider the incentive of each flrm to play an action which leads to the collusive outcome given that all other flrms take the collusive action. If a flrm deviates it earns a proflt ƒ in the current p erio d but it triggers the punishment of the other flrms, which will play the one{shot non{co op erative equilibrium action forever afterwards, by giving the deviating flrm a total discounted payofi of ƒ + – ƒ =(1 ¡ – ). If instead the flrm decides to take D N the collusive action, then it earns a payofi of ƒ (with ƒ < ƒ < ƒ ) in the current p erio d. M N M D W e assume that the existence of a collusive outcome in the industry is p erfectly observed by the antitrust agency , but this is not enough for collusion to b e proved in courts. T o b e able to build a case against the flrms (which would otherwise win the app eal in a Court), the AA needs to flnd some \hard" information ab out collusion. Such information might consist of any do cument proving that flrms have agreed on prices or have met to co ordinate on the prices to b e charged . Perfect observ ability of collusive prices also implies that the antitrust agency will never op en an investigation on flrms which do not collude at equilibrium. F or simplicity we consider the case where flrms decide once and for all at the initial p erio d whether to collude or to deviate from the pro jected cartel . F rom our disc ussion so far, t he t iming of the game, re prese n t ed in Fi gure 1, is as fol lows: and p 2 [0 ; 1], char acteriz ed fo r simpli city b y p osi tiv e and consta n t ma rginal pro ductivi t y . Then the la b or requirement to obtain fi and p are l (fi)= fi=k and l (p)= p= k re sp ectively a nd the to tal cos t of i mpl emen ti ng fi and p are fi fi p p wl (fi)= w fi=k = w fi and wl (p)= wp=k = w p. It wi ll b e clea r in the ana lys is that assuming de creas ing ma rginal fi fi fi p p p pro ductivi t y , which would i mpl y a concave budg et l ine and a conv ex budget set, w o ul d not a lter all o ur co ncl us ions. T o thi s purp os e, no te tha t in our mo del, l ik e a n y rep ea te d g ame with an inflnite hor izon, there exi sts a contin uum of p os sible e quili br ia, and flrms need so me co ordinatio n to sel ect the full y co ll usi v e outc ome g iving them the p er{p eri o d proflt ƒ . In our s etting, this is not a co mpl etely inno cent a ssumption si nce the ga me b ecomes statio na ry o nl y a fter the i ni tial p erio d, once flrms hav e started c oll uding: co ns idering the cho ice of de via ting for any t> 1 is equiv alent, s ince i n this ca se flr ms , havi ng par ti cipated fo r s ome p erio ds to a ca rtel, pay a n exp ected flne ev en if they devia te later o n. When devi ating i ni ti all y , o n the contrary , a flrm can av o id the flne, si nce it never partici pa ted to the il leg al a greeme n t. Howev er, notice that for this rea son a deviati on at the b eg inni ng is mo re attrac ti v e than bre aking down the cartel l ater o n, and the as so c iated co ns tra ints ar e more stringent. Since the a lternative cas e makes the a na lysis more complex but g iv e s the sa me quali tative res ul ts, we have preferred to k e ep the si mpl est v ers ion where flrms decide only a t t = 1 whether to devi ate or col lude. 4 t = 0 The Antitrust Authority determines the p olicy parameters R; fi; p, which are observed by all flrms. The reduced flne R is granted to any flrm co op erating even after the investigation is op ened. t =1 Firms i =1; ::; n decide whether to collude or deviate and realize the p er{p erio d asso ciated payofi. t = 2 The AA op ens an investigation with probability fi 2 [0; 1]. If the inquiry is not op ened, each flrm realizes the p er{p erio d proflts asso ciated to the previous choice. If the investigation starts, flrms simultaneously decide whether to reveal information that the AA will flnd useful to prove collusion; if at least one flrm reveals, the AA is able to prove them guilty . The flrm(s) which co op erated with the AA pays R • F while the others pay the full flne F . If no flrm reveals, the AA is able to prove them guilty with probability p 2 [0; 1]. If the AA has not b een able to prove the flrms guilty of collusion at the end of this inquiry , the flrms will never b e investigated again in the future. If proved guilty , they will b ehave non{co op eratively forever in the future. t> 2 If up to the previous p erio d the AA has not started an investigation, with probability fi it op ens an inquiry in t, flrms decide whether to reveal, and so on. F igure 1 ab out he re W e can now solve for the equilibrium of this game. Our flrst step is to identify the incentive compatibility constraints, which requires to work out, for given p olicy parameters, the subgame p erfect equilibria of the game starting at t = 1, characterized by flrms colluding or deviating and by the choice of revealing or not information to the AA. W e flrst consider the \revelation game" which is played from t = 2 on if an investigation is op ened by the AA. The following Lemma identifles the conditions for the existence of Nash equilibria in which flrms co op erate or not with the AA. Lemma 1Let (1 ¡ p)(ƒ ¡ ƒ ) M N 1 ¡ · – ( p; F ; R)(2) pF ¡ R Pr ovide d that an investigation has b e en op ene d, in the \r evelat ion" game an e quilibrium al way s exist s in which al l flr ms r eve al information. If 1) pF < R or 2) pF ‚ R and – ‚ – (p; F ; R) an e quilibrium exist s in which no flr m r eve als. If this latter exist s, it Par eto dom inates t he e quil ibr ium outc ome in w hich the flrm s r eve al . Pr o of: Se e App endix. 2 5 ~ Figure 2.a b elow illustrates the critical lo cus of p oints –: T o the right of this curve, flrms reveal if an investigation has b een op ened by the AA. T o the left of it, they do not. This curve, which always passes through the upp er right corner of the picture, rotates to the left as the reward from revealing information increases (that is, the lower R) and the larger b ecomes the flne F to b e paid if found guilty: in other words, revelation o ccurs for a wider set of parameters as the incentive to co op erate with the AA is sharp ened. W e can now consider the initial decision to join the prop osed agreement or deviate at t=1. Three p ossible outcomes can o ccur: flrms might prefer not to collude (NC ), since they exp ect an immediate deviation. Alternatively , collusion may start, followed by the decision not to reveal (CN R) or to reveal (CR) if an investigation is op ened by the AA. T o simplify the statement of the results, it is convenient to intro duce the following expressions. – (fi; p; F ) is the v alue which solves: NC –fi(1¡p) ƒ (1 + )+ –fip( ¡ F ) M – ƒ 1¡– 1¡– =ƒ + (3) 1 ¡ – (1 ¡ fi) 1 ¡ – while – (fi; R) is: CR ƒ ¡ ƒ D M · – (fi; R): (4) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N The following prop osition identifles the conditions on the discount factor – for the three outcomes to o ccur. Prop osition 2 For given p olicy p ar ameters (F ; R; fi; p) : † if – (fi; R) • – • – (p; F ; R), fl rms c ol l ude and r eve al if monitor e d (CR). CR † if – ‚ maxf– (fi; p; F ); – (p; F ; R)g, flrm s c ol lude and do not r eve al if monitor e d (CN R). NC † if –< mi nf– (fi; p; F );– (fi; R)g flrm s do not c ol lude (NC ). NC CR Pr o of: See App endix. 2 Figure 2.a b elow illustrates the line corresp onding to – , for given v al ues of fi and R: this CR lo c us do es not dep e nd on p (it is †at) sinc in the region to the right of – flrms co op erate with the AA once an investigation is op ened and p b ecomes irrelev ant. Ab ove the line, flrms prefer to collude even though they anticipate that, if an investigation is op ened, collusion would collapse b ecause flrms would reveal information to the AA. Below the line, flrms, anticipating revelation, prefer to deviate, and the collusive outcome never o ccurs. Consider now – , which identifles the regions where flrms start colluding (ab ove) or not (b elow). NC ƒ ¡ƒ D M For fi =0 of p =0, we have – = – = , and the condition for collusion amounts to NC CR ƒ ¡ƒ D N the \textb o ok" critical discount factor, which is in fact derived under the condition of no antitrust enforcement. Positive v alues of fi and p (and higher v alues of the full flne F ) inc re ase – and make CR the cartel harder to sustain, since the exp ected collusive proflts are reduced. 6 Note also that the more generous the Leniency Program (the lower the reduced flne R)the lowe r – : if flrms exp ect that in case an investigation is op ened they have the p ossibility to reveal CR information and get away with a small flne, this will give an incentive to cho ose the collusive strategy . In other words, a generous Leniency Policy might stimulate ex{ante collusion. (W e shall come back to this issue b elow.) Figures 2.a and 2.b ab out here The curves represented in Figure 2.a deflne, for a given fi, the conditions that must hold for a collusive agreement to emerge, and those which induce revelation or not if an inquiry is op ened by the AA. More precisely , if no Leniency Program is intro duced (R = F ) flrms have no reason to reveal information to the Authority if an investigation is op ened, and the equilibrium outcomes would b e deflned uniquely by the line – : Ab ove the line, flrms would collude (CNR); b elow, they would not NC (NC), b ecause any prop osed agreement would break down immediately . Reduced flnes mo dify the situation: in the region to the left of – flrms don’t reveal if monitored, and the same argument ab ove still applies. T o the right of that curve, flrms anticipate that they reveal information if monitored: below – they prefer not to collude and ab ove they initially collude and then reveal if monitored. CR W e can notice that the conditions for collusion are more demanding with resp ect to the standard case when no AA op erates: the critical discount factor needed for a collusive outcome is always higher than (ƒ ¡ ƒ )=(ƒ ¡ ƒ )when fi and p are p ositive. When a flrm considers whether to join a cartel D M D N or deviate, in fact, it ev aluates the collusive proflts taking into account that with a certain probability collusion will b e detected, inducing a double loss: the flne to b e paid and the lost collusive proflts from there on. The higher the probability of these losses, the lower the collusive proflts. Hence, we need a higher and higher discount factor to balance the temptation to deviate. T o understand the role of Leniency Programs on the sustainability of collusion, consider what happ ens when, starting with a situation in which no Leniency Program is used, we intro duce reduced flnes. This has two efiects which are shown in Figure 2.a. On the one hand, the Leniency Program might have an adverse, pro{collusive efiect. By reducing the exp ected v alue of the flne to b e paid if an investigation is op ened, the Leniency Program might give an incentive to collusion. This o ccurs in the area (1) included b etween the dotted part of the curve – and the line – . In this region, no NC CR collusion can b e sustained in the industry if full flnes are given (NC), but under a Leniency Program flrms would engage in collusion and, if monitored, they would reveal (CR) and pay the reduced flne R< F . On the other hand, there exists an area (2) where collusion will break down (b ecause the flrms reveal information) if the AA starts monitoring the industry (CR), whereas in the absence of a Leniency Program collusion could stop only after a successful complete investigation (CNR). This is the area comprised b etween the dotted part of the curve – and the curve – . . NC W e can now move to the analysis of the optimal p olicy , having identifled the implementable allo cations. So far we have expressed the conditions for the difierent equilibrium outcomes in the If the Le ni enc y P rogra m w e re una n tic ipated, flrms would decide whe ther to co llude or no t on the ba sis of an exp ected flne R = F and therefore w o ul d not co o p erate unl ess – ‚ – . When the l eni ency progra m is intro duc ed une xp ectedly , N C co llusio n w o uld break down in all the area b el ow the curv e – (that is , (1 ) plus (2)), without an y adv ers e efiec t ari sing. 7 space (p; – ): this was useful b ecause we obtained the conditions of cartel stability in terms of critical discount factors, thereby allowing a comparison with the mo dern theory of collusion. T o pro ceed with the analysis of the optimal p olicy design, it is convenient to rewrite the critical lo ci found ab ove in the spac e (p; fi) of p olicy parameters. Firms would reveal if monitored if: ƒ ¡ ƒ + R(1 ¡ – ) M N p ‚ =~ p( –; R ; F ): (5) ƒ ¡ ƒ + F (1– ) M N Firms would prefer to collude rather than deviate, when they anticipate that the op ening of an investigation would result in collusion broken down by revelations, if: ƒ ¡ ƒ + – (ƒ ¡ ƒ ) M D D N fi • = fi (–; R): (6) CR – (ƒ ¡ ƒ + R) D N Finally , collusion arises in the case where flrms anticipate that no revelation would o ccur after the op ening of an investigation, if: (1 ¡ – )[ƒ ¡ ƒ + – (ƒ ¡ ƒ )] M D D N fi • = fi (–; p; F ): (7) NC – [ pF (1 ¡ –)+ p(ƒ ¡ ƒ )+ ƒ (1 ¡ – ) ¡ ƒ + – ƒ ] M N D M N The three lo ci ab ove allow to deflne, in the space of p olicy parameters, three regions asso ciated with difierent implementable allo cations, in which flrms do not collude (NC), collude and reveal if monitored (CR) and collude and do not reveal (CNR): A = f(fi; p) 2 [0; 1] j fi ‚ maxffi (p);fi gg (8) NC NC CR A = f(fi; p) 2 [0; p ~ ] £ [0; 1] j fi< fi (p)gg (9) CN R NC A = f(fi; p) 2 [0;fi ] £ [~ p; 1]gg (10) CR CR When no Leniency Program is intro duced the only outcomes are NC, if (fi; p) are ab ove the fi NC curve, or CNR otherwise. If R< F the threshold p ~ b ecomes lower than 1 and CR is an outcome if fi< fi and p> p ~ . Notice that fi (~ p)= fi , that is the upp er left corner of the region asso ciated CR NC CR to CR shifts up along the fi curve as R is reduced. When R = 0 we obtain the widest CR region. NC W e flnd also in the (fi; p) space the same adverse efiect of Leniency Programs already discussed: the intersection of A when R = F and A when R< F is non empty . That means that there are NC CR p olicy combinations which prevent collusion when full flnes are given and that induce flrms to collude and reveal once a Leniency Program is intro duced. ƒ ¡ƒ D M Moreover, if –< , where the latter term is the standard critical discount factor for col- ƒ ¡ƒ D N lusion when no antitrust prosecution is considered, fi < 0and fi < 0, i.e. the only admissible NC CR outcome for any v alue of the p olicy parameters is NC. Figure 2.b illustrates the equilibrium outcomes ƒ ¡ƒ D M when –> and R< F , and it is the dual of flgure 2.a - see ab ove. ƒ ¡ƒ D N W e summarize the subgame p erfect equilibrium outcomes of the sup ergame played by flrms for given p olicy parameters and discount factor – in the following prop osition, which is the dual of Prop osition 2. Prop osition 3 Given t he gains ƒ and ƒ s p e cifle d ab ove, M D 8 † If the p ol icy c ombination (fi; p) 2 A ther e is a un ique sub game p er fe ct e quilibrium in which NC flr ms wil l abstain ex{ant e fr om c ol l usion ( NC). † If (fi; p) 2 A t her e is a unique sub game p erfe ct e quilibrium in which flrm s c ol lude and don ’t CN R r eve al if m onitor e d (CNR). † If (fi; p) 2 A ther e is a unique sub game p erfe ct e quilibrium in which flr ms c ol lude and r eve al CR if monit or e d (CR).If R = F , A is an empty s et . CR The AA cho oses (fi; p; R)given the incentive compatibility constraints, summarized in Figure 2.b and Prop osition 3, in order to maximize a utilitarian welfare function in which flnes are pure transfers. Let K = DW L=(1 ¡ – ) b e the discounted sum of the deadweight loss DW L, which can b e thought of as the net so cial b eneflt from ppreventing collusion Moreover, let W b e the present v alue of the welfare gain if the p olicy induces the equilibrium outcome j = NC; C R; C N R. Then we have, for given (fi; p), W = K> W = fiK =(1 ¡ – (1 ¡ fi)) >W = fipK =(1 ¡ – (1 ¡ fi)). NC CR CN R It is useful to identify the (welfare) indifierence curves for the p olicy problem in the (fi; p) space: if we do not intro duce flne reductions, in all the region A we have full deterrence ex-ante and the NC asso ciated welfare gains are K for all the p olicy parameters in the A re gion. In t he re gi on A NC CN R the indifierence curve for a level of welfare gains W is fi = W (1 ¡ – )=(pK ¡ – W ), i.e. it CN R CN R CN R is a decreasing and convex curve in the (fi; p) space: ex{p ost desistence in this case dep ends on b oth fi and p according to the trade{ofi describ ed by the curve. F igure 3 ab out he re Moreover, it is easy to show that the indifierence curves in the A region have a shap e similar CN R to the fi curve as deflned in ( 7), which is the upp er b oundary of that region, and in the limit they NC overlap with that curve. In fact, if we consider the indifierence curves for given W and the fi (p) CN R NC curve which is the upp er b oundary of the A region and equate them we obtain after rearranging: CN R W – (ƒ ¡ ƒ ) ¡ (ƒ ¡ ƒ ) CN R D N D M = · p ^ K – (F (1 ¡ –)+ ƒ ¡ ƒ ) M N The right hand side expression corresp onds to the upp er intercept of the fi (p) curve at fi =1, NC i.e. fi (^ p) = 1. Hence, lo oking at the expression ab ove, if W =^ pK the indifierence curve NC CN R overlaps with the upp er b oundary of the A region, that is with the fi (p). F or W < pK ^ CN R NC CN R the indifierence curve in the A region shifts toward the origin. CN R When a Leniency Program is intro duced, b elow the A region we have the A and A NC CR CN R regions. The indifierence curves across the region A are fi =(1 ¡ – )W =(K ¡ – W ): those CR CR CR curves are horizontal, since in the CR case ex{p ost desistence dep ends only on fi. The same level of welfare in the A region can b e obtained only if fi is higher; that means that the indifierence curve CN R is discontinuous at p ~ and jumps up as we move from the A to the A region . CR CN R Notic e that W = W fo r the s ame fi when p = 1 . Hence, i f we extend the W indi fierence curve in the A CN R CR CN R CR reg ion up to p = 1 we flnd the level o f fi such that W = W and we are able to iden ti fy the l ev el of the indi fie renc e CR CN R curv e in the A regi on, as shown in flg ure 3. CR 9 The iso{welfare curves in the A and A regions do not identify a convex set of p olicy CN R CR parameters. W e pro ceed therefore convexifying the indifierence curves in the following way . Consider an indifierence curve in the A and A region; draw a line which passes through the p oint of CN R CR discontinuity (fi =(1 ¡ – )W =(K ¡ –W );p =~ p) and which is tangent to the indifierence curve in CR CR the A re gion. Le t t he tange nc y p oi nt b e e(W ); rep eating this precedure for difierent v alues CN R CN R of W an entire lo cus e(W ) is obtained. Deflne E the subset of A to the left of that CN R CN R CN R CN R lo cus, which is represented in Figure 3. Notice that, constructing E , we have excluded those CN R p oints on the indifierence curves in the A region which are dominated by a combination of p olicy CN R parameters in (at the b oundary of ) the A region, obtaining a convex set of p olicy parameters. CR W e can now analyze the optimal p olicies. According to the v alues of B; w and w , i.e. the fi p p osition of the budget constraint B = w fi + w p in the (fi; p) space, we can have difierent solutions fi p to the optimal p olicy problem. Prop osition 4 Con sider the optimal p olicies given the budget c onstr aint. † If the budget c on str aint is ab ove or on the fi (p) cur ve, the optimal p olicy implements NC at NC a tangency p oint b etwe en the budget c onstr aint and the fi (p) curve, and the set of p ossible NC e quilibrium outc omes incl udes al l the cur ve, i.e. E = f(fi; p) j p 2 [0; 1];fi = fi (p)g. NC NC † If the budget c onstraint is b elow the fi (p) curve the optimal p olicy implements either CR or NC CNR. { In a CR e quilibrium the optimal p olicy sets R =0, p =~ p and fi along the budget constr aint, and the p olicy c ombinations lie along the vertic al line p ~,i.e. inthe set E = f(fi; p) j fi 2 CR [0;fi ];p =~ pg. CR { In a CNR e quilibrium the optimal p olicy combinations are at the tangency p oint b etwe en the budget c onstraint and the indifierenc e curve. † If the budget constr aint is tangent to an indifier enc e curve in the E re gion deflne d ab ove, CN R the optimal p olicy implements a CNR outc ome; otherwise CR is the e quilibrium outc ome. Pro of: See App endix. 2 Prop osition 4 gives the conditions which in general allow to identify the optimal p olicies for given budget constraint and it deflnes three sets of p olicy parameters which corresp ond to the difierent equilibrium outcomes, as represented in Figure 3. It is useful to consider the sequence of p olicy regimes that are asso ciated with lower and lower budget constraints. Notice that two p ossibile sequences can arise, according to the way in which the budget constraint shrinks: either we move from a NC to a CNR regime, if the budget constraint is initially very steep and the tangency p oint on the fi (p) NC curve which implements the NC outcome lies in the neighb orho o d of the E region, or we have, CN R for atte r budget constraints, a NC-CR-CNR sequence if the tangency p oint with the fi (p)curve NC is in its lower part. This latter case seems quite interesting and allows to get the intuition of the pros and cons of the Leniency Programs. Consider the optimal p olicies for parallel shifts of the budget constraint; for a relatively high total endowment a NC outcome can b e implemented at a tangency p oint with the fi (p)curve: in NC 10 this case reduced flnes would b e harmful, inducing collusion (and revelation) when otherwise the AA would b e able to prevent collusion. When the budget constraint shifts downwards and lies b elow the A curve, it is no longer p ossible to obtain ex-ante deterrence of collusion. In this case it is optimal to NC implement a CR outcome by granting maximum flne discounts and setting the p olicy parameters along the p ~ vertical lo cus: intuitively , when the AA is only able to implement ex-p ost desistence, reduced flnes b ecome app ealing as a less costly way of proving and interrupting collusion. The implicit cost of such a p olicy is the need to sink resources in order to make indep endent prosecution a credible threat which induces revelation. As a consequence, when the total endowment is further reduced (the budget constraint shifts further downwards), fewer and fewer resources are left for general monitoring, which in the end determines the likeliho o d of interrupting collusion and the desirability of such a p olicy . At some p oint, we flnd that the (low) budget constraint b ecomes tangent to the iso{welfare curve in the E region: it means that we obtain a higher exp ected welfare moving to the region where CN R flrms collude and do not reveal, abandoning the Leniency Program and changing the mix of p olicy parameters in a more favourable way . 3 Alternative Leniency Rules In this section we adapt the model to alternative Leniency Rules that have b een adopted in the recent exp erience in the US and in the Europ ean Union. The flrst extension refers to the p ossibility of giving reduced flnes only if flrms reveal information b efor e an inquiry is op ened by the AA. Another regime assigns the reduction in flnes only to the flrst flrm which ofiers co op eration with the agency . Next, we suggest that if only one sp e ciflc flrm is entitled to b eneflt from a Leniency Program, this p olicy would b e even more successful. 3.1 Fine reductions only before the inquiry is opened As mentioned in the intro duction, the initial Leniency Program intro duced in the US in 19 78 entitled flrms with a reduction in flnes only if the co op eration started b efore an inquiry was op ened. On the same line, the actual regime chosen in the EU with the July 1996 Notice is more favourable for flrms who reveal information b efore the AA has op ened an o–cial investigation. It is therefore interesting to analyze whether this rule can b e justifled in terms of enforcement efiectiveness. W e show that this is not the case. Let us consider a \flne reductions only b efore an inquiry is op ened" regime. The corresp onding game structure is describ ed for the general case of n flrms in the following : t = 0 : The AA sets the p olicy parameters fi ; p; R which are observed by the flrms. t =1 : Firms i =1; : :; n decide whether to collude or deviate and realize the asso ciated payofis. t = 2 : At the b eginning of the p erio d, flrms simultaneously cho ose whether to reveal the existence of the cartel to the AA, b enefltting of reduced flnes, or not; if no flrm reveals, the AA op ens an investigation with probability fi 2 [0; 1], provi ng t he m gui lty wit h probabil ity p 2 [0; 1]. Then, payofis are realized. The pay ofis in the di fie ren t o utco mes a re s imil ar to the mo del a na lysed ab ove, and wil l b e o mitted he re in the descri ptio n o f the ga me. 11 t> 2 : if up to the previous p erio d the AA has not started an investigation, the game restarts as from t = 2, etc. Consider flrst the subgame starting at t = 1 after a decision to collude. T o flnd the conditions under which not revealing is an equilibrium, we have to compare the payofi from revealing when the other flrms do not reveal, namely ¡ R, with the payofi from not revealing when the other flrms 1¡– do not reveal. The latter is given by: ƒ ƒ N M ƒ = fi[p( ¡ F )+(1 ¡ p)( )] + (1 ¡ fi)(ƒ + – ƒ ); nr nr 1 ¡ – 1 ¡ – whence: ƒ ƒ N M fip( ¡ F ) + [(1 ¡ – + fi( – ¡ p)] 1¡– 1¡– ƒ = : nr 1 ¡ – (1 ¡ fi) ƒ ƒ N M It is simple algebra to check that this payofi is higher than (p( ¡ F )+ (1 ¡ p) ), the 1¡– 1¡– exp ected payofi from not revealing after the investigation has b een op ened, which was the relev ant one under the rule analyzed in the previous section. Since the payofi from revealing is the same in b oth cases, it follows that the equilibrium where flrms do not reveal is more likely to o ccur when the Leniency Program is applied only for revelations b efore the inquiry is op ened. In other words, the curve – moves to the right and collusion is less likely to b e broken by revelations in this regime. This is hardly surprising, b ecause the probability of the event \b eing found guilty and thus flned" is lower b efor e seeing if the industry will b e monitored than after an investigation is actually op ened. W e have now to consider if the Leniency Program might change the ex{ante incentives of flrms to collude. It turns out that there would never b e collusion in the industry when flrms exp ect that there would b e revelation of information to the AA in the following p erio d: this implies that an equilibrium in which flrms cho ose to collude and reveal do es not exist. In fact, by colluding when exp ecting the cartel to b e broken by information given to the AA, a flrm would get V =ƒ + – (ƒ =(1 ¡ – ) ¡ R). c M N By deviating, it would get V =ƒ + – ƒ =(1 ¡ – ) . Si nce ƒ > ƒ and R ‚ 0, it follows that d D N D M V <V . c d In the case, considered in the previous section, where flrms were entitled to flne discounts aft er the op ening of an investigation, the exp ected proflt from collusion decreases when the event \op ening of an investigation" realizes, leading flrms to reveal information to the agency . In the case we are considering here, instead, nothing new happ ens b etween the moment when the flrms decide on collusion and the moment when they are asked to co op erate with the authorities to break down the cartel. Our analysis reveals that if Leniency Programs are to b e efiective in breaking down cartels, they should b e extended to b eneflt flrms which reveal after the industry is put under monitoring. Since proving flrms guilty of collusion is a very lengthy and complex issue, which do es not always end up with the flrms b eing condemned, a great amount of resources can b e saved and a flnal p ositive outcome guaranteed by ensuring that flrms have the prop er incentives to collab orate with the AA even after an investigation has b een started. Allowi ng flrms to cho ose whethe r to reveal or no t b e fore an inv es tiga tion i s op ened at a n y p erio d w o ul d not cha ng e the res ul ts. 12 This result is consistent with the US exp erience, where initially the Leniency Program was used only for flrms which sp ontaneously ofiered evidence b efore the inquiry was op ened by the AA. In this initial regime the program was quite inefiective while, once allowed in 1993 for reduced flnes even after the inquiry was op ened, the numb er of cases in which flrms co op erate with the judges increased signiflcantly . In the 1994 Annual Rep ort of the Antitrust Division it is stressed that in the flrst year of the new regime \an average of one corp oration p er month come forward with information on unilateral conspiracies, compared to an average of one p er year under the previous p olicy . The p olicy thus allowed the Division to extend the reach of its criminal enforcement activities with relatively little exp enditure of resources" . According to our results, the new regulation on Leniency Programs adopted by the EU should b e widened. The regulation states that flrms which denounce a cartel b efore the Commission has op ened an investigation are entitled to a reduction of 75{100% of the flnes. Firms which denounce a cartel after that a \veriflcation" has b een op ened are entitled to a 50{75% reduction of the flnes, but only if those veriflc ation s had not b e en fruitful and had not led to the op ening of a pro cedure. Basically , this means that Leniency Programs are op ened only for flrms op erating in industries which are not under the scrutiny of the AA. This narrows to o much the scop e of the application of the regulation, and fails to provide the flrms with enough incentives for revealing information which can b e useful to break the cartel. 3.2 Only the ¯rst comer obtains a ¯ne reduction The criteria that determine which flrms can receive the b eneflts of a reduced flne have b een restricted in difierent ways b oth in the US and in the EU exp erience. An interesting case is where only the flrst flrm which ofiers evidence is given a flne reduction, as it is the case in the EU regulation. In this case the game structure is the same as in our initial mo del. The only difierence is that if all flrms decide to reveal information to the judges, as it happ ens in a subgame p erfect equilibrium in which flrms reveal if monitored, the exp ected payofi b ecomes: ƒ R +(n ¡ 1)F ¡ (11) 1 ¡ – n where n is the numb er of flrms in the cartel: every flrm is ex{ante the flrst one to disclose information to the AA with probability 1=n. Notice, however, that when we check for the existence of an equilibrium in which no flrm reveals, a deviating flrm obtains the reduced flne R for sure, b eing the only one which co op erates with the judges. Hence, the condition for an equilibrium in which no flrm reveals is – ‚ – , exactly as in the case treated ab ove. Moreover, it is easy to see that if an equilibrium exists in which no flrm reveals if monitored, it also Pareto dominates the equilibrium in which all flrms co op erate with the AA. Anti trust Divi sio n (19 94), p.6 {7. See O–cial Journal of the Europ ean Communities , Seri es C, 2 07, 1 8{ 7{1 998 . T a ken litera lly , o ur anal ys is wo ul d al so sugg est tha t when flrms reveal they s ho ul d al ways recei ve a zero flne ( R =0), si nce this wo ul d gi ve them the g reates t incentive to deno unce the ca rtel. Howeve r, we a re a ssuming tha t co lla b orati ng wi th the AA is a binary v ari able. E ithe r o ne do es not coll ab ora te, or i f it do es i t ca n g ive a ll the info rmatio n necess ary to prove the pa rticipa ti on in the cartel of all the flrms . In rea lity , the typ e of info rmatio n that flrms ca n provide would b e more of a continuo us v ari able, and tuning the flne re ductio ns to the quali ty of the info rmatio n reveal ed make s sense. 13 ~ Consider now the decision of flrms on collusion at t =1: if – ‚ – flrms will not reveal if monitored and everything is as in the basic mo del. However, if –< – , revelation will follow the op ening of an investigation, but flrms’ incentives to collude are mo difled in the present regime, since the exp ected payofi if monitored is lower than in the previous case where all flrms could b eneflt from the Leniency Program. One can check that flrms will abstain from collusion ifi ƒ ¡ ƒ D M – ‚ eq ui– (12) CR R+(n¡1)F (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fi( ) D N It is immediate to notice that – <– , that is, the region of parameters that induce flrms to abstain CR CR from collusion is larger than in the previous \all flrms get the reduction" regime | see Figure 4. F igure 4 ab out he re The intuition of this result is as follows: in the more restrictive set of rules analyzed in this section, the exp ected reduction in flnes is smaller when all flrms cho ose to coop erate with the judges, although it is equiv alent when we consider the incentive for a flrm to cheat the partners when they do not reveal. Hence, when flrms anticipate that they all will confess if monitored, they exp ect higher sanctions. Consequently , in some cases they flnd it less attractive to collude and re ve al as an alternative to deviating from the b eginning and avoiding the flne. The regime therefore is able to partially reduce the ex{ante incentive to collusion without reducing the p ower of the program in making flrms denounce a cartel after an inquiry is op ened. This case suggests an alternative rule which might increase the efiectiveness of a Leniency Program, by further reducing the ex{ante incentive of engaging in collusion induced by the exp ected reduction in flnes. 3.3 Only a speci¯c ¯rm receives a ¯ne reduction As we have rep eatedly emphasized, a Leniency Program inuences flrms in two ways. The flrst is that it stimulates ex{p ost breaking of the cartel via revelation of information to the AA; the second (adverse efiect) is to increase the incentive of collusion via a reduction in the punishment in case of b eing found guilty . W e have also seen that granting a reduction in flnes only to the flrst flrm which reveals works b ecause it leaves unchanged the flrst efiect but reduces the second. The efiectiveness of the Leniency Program could b e increased even further by increasing asymmetries in the industry and sp ecifying ex{ante that only a sp eciflc flrm could b e entitled to the LP , no matter the way in which such a flrm is selected. The way of interpreting this rule is that of deflning ex{ante a set of parameters which allow all the participants in each sp eciflc situation to identify a single flrm entitled to a reduced flne : the flrms involved in the cartel, applying the rule, are able to work out which one will b e the flrm selected. Denote this flrm with a numb er, say 1. The conditions under which revelation o ccurs are the same as usual: If –< – , the cartel would break b ecause flrm 1 denounces it. On the other W e thank P . Rey fo r s ug ges ti ng this extensio n. F or insta nce, i t mi gh t b e the flrm lo cated in the smal lest city , o r the l ast one in a lpha b etica l o rder, etc. 14 hand, the conditions under which ex{ante collusion o ccurs will change. F or the n ¡ 1 flrms which are not entitled to the Leniency Program, the condition for taking part in the collusion will b e: ƒ ¡ ƒ D M – ‚ · – (13) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiF D N F or flrm 1, the c ondit ion is laxe r: ƒ ¡ ƒ D M – ‚ (14) (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N However, since all the flrms must flnd it convenient to take part in collusion, the latter condition does not play any role, while the former is binding and determines the existence of collusion. Also, F I notice that – >– >– | see Figure 4. In other words, if the authority targets the Leniency CR CR CR Program to a sp eciflc flrm, it will b e able to reduce the ex{ante adverse efiect of it without decreasing the ex{p ost incentive to reveal information. Hence, collusion b ecomes less likely b ecause the flrms excluded from the program flnd it less app ealing to engage in a cartel which includes a likely cheater . 4 Heterogeneous Cartels So far we have considered homogeneous cartels, in which the payofis in each p ossible outcome were the same across partners. Notice however that, in all our arguments, if the participants have heterogenous payofis and they know the payofis of the partners in each p ossible outcome, the equilibria are governed by the conditions of one of the flrms, the one whose constraints bind. This decisive agent is the p oint of reference for the others, whether they exp ect such flrm to deviate or to reveal information after colluding, and drives the equilibrium conditions of the entire cartel. Hence, in a sense, our previous analysis allows to consider heterogeneous flrms within a cartel, but it assumes that in each cartel in the economy such a decisive agent is always the same. It is therefore interesting to consider the case in which the cartels are truly heterogeneous, in the sense that the participants may difier in payofis and the decisive partner may b e difierent across cartels. W e consider in this setting the design of an optimal enforcement p olicy which cannot b e made conditional on cartel’s typ e, due to informational and/or institutional restrictions. Hence, the AA has to design a single, general p olicy facing many difierent industries, characterized by heterogeneous market conditions and p otential gains from collusion. In this case, the p olicy implemented will induce difierent efiects in the v arious industries, reaching a more or less efiective deterrence of collusion and inducing difierent typ es to cho ose difierent reactions: hence we might have some cartel typ es colluding and not revealing while others will prefer not to join the cartel; or we might have all typ es colluding, but only a subset of them revealing information when monitored, etc. Hence, the difierent efiects that we have identifled in the previous sections will b e combined in a richer way once the AA faces heterogenous typ es. F rom the previous analysis we already know that the incentive compatibility constraints for given p olicy parameters dep end on two v ariables of cartel’s typ e: ƒ ¡ ƒ and ƒ ¡ ƒ . Hence, M N D N Of course , l eniency rules which limi t the a ppli cabil ity of the flne re ductio n to only one flr m wi ll res ul t in a l arg er amo unt of money c oll ected thro ug h flnes. In a w orl d where non{disto rtionary transfers ar e no t av a ila bl e, this would b e an addi tional a dv anta ge of s uch rul es. 15 multiple typ es would require to deal with a biv ariate distribution, related to the gains from collusion and from deviation. T o maintain the analysis simple, we assume in this section Bertrand comp etition (with constant marginal costs ) in the non{co op erative equilibrium: hence ƒ =0 and ƒ = nƒ : N D M the gains from collusion are now p erfectly correlated to those from deviation, and we can consider a univ ariate distribution of typ es. Cartel typ es refer to the gains from collusion, due for example to difierent marginal cost levels, with ƒ 2 [ƒ ; ƒ ]; the AA do es not observe cartel typ es but M M knows their distribution g (ƒ ), and is not able to condition the p olicy chosen to some observ able that can make it contingent on a message. In other words, the AA sets a single combination of p olicy parameters taking into account that there exist many cartel typ es in the economy . Under the assumption of Bertrand comp etition the standard critical discount factor when an- titrust is absent, – =(ƒ ¡ ƒ )=(ƒ ¡ ƒ ), is (n ¡ 1)=n. W e can rewrite the relev ant lo ci as: D M D N ƒ (1 ¡ n + n– ) fi = =(– ¡ – ) =– CR ƒ n– which do es not dep end on cartel’s typ e, (1 ¡ – )n(– ¡ – )ƒ fi (p)= NC – [pF (1 ¡ –)+ƒ (p ¡ n(– ¡ – ))] and p ~ = (ƒ + F (1 ¡ – )) which are b oth increasing in ƒ . Moreover, fi is always ab ove fi at p = 1. Hence, when R< F M CR NC we can distinguish 5 regions which are represented in flgure 5. F igure 5 ab out he re fip In region A all typ es cho ose CNR and the corresp onding welfare is W = E (K ) whe re 1¡– +fi– E (K ) is the exp ected v alue of the gains from deterrence given the distribution of typ es g (ƒ ). In region B all typ es cho ose CR with W = E (K ) while in E all typ es abstain from collusion and 1¡– +fi– welfare is W = E (K ). In region C some typ es cho ose CNR and others CR: let ƒ be thetypewhose p ~ equals the p chosen by the AA in region C: all typ es lower than ƒ c oll ude and re ve al whil e t he cartels more profltable collude and don’t reveal. The exp ected welfare is therefore Z C Z ƒ ƒ fi M fip W = K (ƒ )g (ƒ )dƒ + K (ƒ )g (ƒ )dƒ C M M M M M M 1 ¡ – + fi– 1 ¡ – + fi– ƒ ƒ M M Analogously , in region D lower typ es abstain from collusion and higher typ es collude and don’t reveal, with the threshold typ e ƒ such that the actual p olicy combination in D lies on that typ e’s fi (p) NC curve. The exp ected welfare is then Z Z ƒ ƒ fip W = K (ƒ )g (ƒ )dƒ + K (ƒ )g (ƒ )dƒ D M M M M M M 1 ¡ – + fi– ƒ ƒ When R = F only regions A,D and E exist, deflned by the set of fi (p) curves which extend N C up to p =1. 16 The analysis of the optimal p olicy pro ceeds in three steps, which are develop ed analytically in the App endix. First, the iso{welfare curves in each of the flve regions A{E are derived; then, we check how the same welfare level is obtained passing (eventually) from one region to the neighb ouring one, distinguishing whether flne reductions are given or not; flnally , comparing the two cases, it is selected whether reduced flnes R allow to save enforcement costs, deflning a set of iso{welfare curves along which Leniency Programs are optimally used. The result of this analysis is shown in flgure 6.a: the lower b old curve is the iso{welfare (cost minimizing) curve setting R = 0, which passes through the regions A{C{B. The upp er b old curve passing in the D{C{B regions entains the use of reduced flnes only in a subset of the B and C regions. The p olicy combinations (R; fi; p) which minimize the cost of reaching the same exp ected welfare are summarized in a map of iso{welfare curves which are not convex: as b efore, we have to convexify them excluding from the set of p ossible equilibrium outcomes those p olicy combinations which b elong to the non{convex p ortions of the indifierence curves. Given the map of indifierence curves that minimize the cost of a given exp ected welfare, we exclude those p ortions which can never b e selected given our linear budget constraint .For the indifierence curves in the A region we obtain a subset of p oints E analogous to the one obtained CN R CR in the single typ e case already discussed. In region C we flnd a subset of p oints E in which some CN R typ es cho ose CR and higher typ es cho ose CNR. In region B we select only the b oundary to the left, CR NC which corresp onds to the E case when all typ es opt for CR. A subset of D, E is obtained CN R CN R where low typ e select NC and high typ es cho oase CNR, and flnally from region E we select the lower b ound. Once excluded the non{convex p ortions of the iso{welfare curves, the optimal p olicies for given budget constraint can b e established along the same lines of Prop osition 4’s pro of. W e summarize the results in the following Prop osition, which is respresented in flgure 6.b. Prop osition 5 Consider the optimal p olicy under asymmetric information given the budget c onstraint and the distribution of c artel typ es. † If the budget c onstraint p asses through re gion E, the optimal p olicy implements NC for al l typ es at a tangency p oint betwe en the budget c onstraint and the fi (p) curve of the highest typ e. N C NC † If the budget c onstraint p asses through re gion D and is tangent to an indifier enc e curve in E , CN R the optimal p olicy is at the tangency p oint with no flne re duction, and implements a CNR{NC outc ome ac c ording to the difierent typ es. † If the budget c onstraint p asses through re gion A and is tangent to an indifierenc e curve in E , CN R the optimal p olicy is at the tangency p oint and implements CNR for al l typ es. CR † If the budget c onstraint p asses thr ough C and is tangent to an indifierenc e curve in E ,that CN R is the optimal p olicy and implements a CNR-CR outc ome. † In al l the other c ases the optimal p olicy implements CR for al l typ es setting p e qual to the p ~ of the highest typ e along the budget c onstraint. An y c onv ex budg et s et, a s tha t o btai ne d under the as sumptio n of decr easi ng re turns to enforce men t, w o ul d al low a si mila r exerci se. 17 Figures 6.a and 6.b ab out here W e can give an explanation of the result ab ove considering the sequence of optimal p olicies when the budget constraint b ecomes steep er and steep er as a result of an increase in the cost of indep endent prosecution (higher w ). F or low v alues of w the p olicy implements full deterrence ex{ante for all p p typ es. As the budget constraint rotates toward the origin we initially move to a CNR{NC mixed outcome with no flne reduction, in which the more profltable cartels are not deterred. Granting flne discounts in this case would shift low typ es from NC to CR: the pro{collusive efiect of Leniency Programs would dominate reducing welfare. However, when the fraction of low typ es which cho ose NC shrinks further, reduced flnes are intro duced, inducing all typ es to collude and reveal. In this case the improvement in prosecution allowed by reduced flnes b ecomes predominant. A further increase CR in w moves the equilibrium outcome in the E region with an increasing p ortion of high typ es CN R that cho ose CNR while low typ es collude and reveal. The implicit cost of the Leniency Programs, which forces the AA to commit resources to indep endent prosecution to make it a credible threat, b ecomes heavier and heavier as the resources left to op en inquiries decrease and as the fraction of typ es which are induced to reveal shrinks. In the end we move to the E region, abandoning the CN R Leniency Program. Hence, the optimal p olicy is determined, in a sense, by the relative imp ortance of the pro{welfare efiect of Leniency Program, that allows to obtain more efiective ex{p ost desistence, and the welfare decreasing efiects of reduced flnes: the incentive to collude (and reveal) instead of abstaining from collusion, and the need to sink resources to make indep endent prosecution credible, which reduces the probability of op ening an inquiry and of obtaining ex{p ost desistence. 5 Conclusions In this pap er we have analyzed the efiects of Leniency Programs on the incentives of flrms to collude and to reveal information that helps the Antitrust Authority to prove illegal b ehaviour. The b enchmark regime gives to any flrm a reduction in flnes even if revelation o ccurs after an investigation is op ened. W e show that reducing the exp ected flnes may induce a pro{collusive reaction: combinations of p olicy parameters which, without Leniency Programs, would prevent collusion, may induce flrms to collude (and reveal if monitored) when flne reductions are given. Hence, if the resources av ailable to the AA are su–cient to prevent collusion using full flnes, Leniency Programs should not b e used. However, when the AA has limited resources, Leniency Programs may b e optimal in a second b est p ersp ective. Fine reductions, inducing flrms to reveal information once an investigation is op ened, increase the probability of ex{p ost desistence and the exp ected welfare gains. The optimal scheme requires maximum flne reductions and a shift of resources from prosecution to monitoring. A flxed amount of resources, however, must b e committed in any case to make indep endent prosecution a credible threat, since no flrm would reveal if it exp ects that the AA is unable to prove them guilty . When indep endent prosecution is very costly , to o few resources are left to general monitoring, which in the end determines the efiectiveness of Leniency Programs. In this case it may b ecome more convenient to shift back to a full flnes regime with a more favourable mix of p olicy parameters. W e have then compared our b enchmark regime with alternative sets of rules: the flrst allows to give flne reductions only to flrms which co op erate with the Antitrust Authority b efore an inquiry 18 is op ened, as initially established in the US p olicy in 1978, and similar to the approach followed by the EC Notice on the non-imp osition of flnes, and we proved this regime to b e inferior with resp ect to our b enchmark case. W e have then considered other rules which restrict the set of the flrms that can b eneflt from a Leniency Program. W e showed that by granting a flne reduction only to the flrst flrm which co op erates with the AA the p erverse pro{collusive efiect of the Leniency Program would b e reduced without softening the incentives to reveal information. Better still, the AA might target a sp eciflc flrm and allow only this one to b eneflt from the reduction. The intuition for this result, which makes the Leniency Program even more efiective, lies in the asymmetry that the p olicy intro duces among otherwise identical flrms, b etween the entitled flrm and the excluded ones: the latter would more often prefer to abstain from collusion rather than join a cartel together with a likely cheater. Finally , the case of multiple cartel typ es has b een considered: the AA is assumed to b e unable, for informational or institutional reasons, to implement Leniency Programs contingent on cartel’s typ e, and therefore has to set general rules. F or instance, the AA cannot shap e the p olicy to the conditions of each sp eciflc industry , but has to cho ose a general rule of b ehaviour, obtaining difierent efiects in difierent industries. Then, according to the p osition of the budget constraint in the set of p olicy combinations, we characterized the optimal p olicy: it turns out that the p olicy parameters and the regime of full or reduced flnes are chosen according to the relative weight of the three efiects describ ed ab ove, where the weights dep end on the share of typ es which cho ose the difierent equilibrium outcomes (no collusion; collusion; collusion and revelation). W e b elieve that, despite the simple setting, our pap er sheds some light on the desirable features of leniency programs, and suggests some changes in the EC leniency p olicy . First of all, if it is optimal to use a leniency program (as in the realistic case where the antitrust agency has limited resources), then the program should b e as generous and certain as p ossible with the flrms which provide fresh evidence that establishes the existence of a cartel. In contrast, the EC p olicy of keeping some degree of discretionality instead of granting automatic and total reduction of flnes even to those flrms which fulfll all the (strict) conditions laid down in the EC Notice undermines the success of the leniency program, as it does not give certainty to the prosp ective co op erating flrm and reduces the incentive to break the cartel. Likewise, some of the conditions required by the EC p olicy are to o strict. F or instance, a flrm must \maintain continuous and complete co{op eration throughout the investigation" to b e entitled to have a very substantial reduction (more than 75%) of the flne. This has led the Commission to give only a 50% reduction to a flrm, T ate & Lyle, which had sp ontaneously brought conclusive evidence of a cartel to the attention of the Commission (at a time when the Commission did not even susp ect the existence of an agreement), but had later (partially) contested some of the allegations made by the Commission . The strict wording and application of the Notice will reduce the incentive of the flrms to reveal information . F urthermore, our analysis indicates that a leniency program should b e equally applicable to information disclosed b efore and after an investigation has started, whereas the EC p olicy do es not Thi s is the ca se \Br itish Suga r", EC Deci si o n of 14 Octob er 199 8, publi shed i n the O–cia l Journal o f the EC, L76, 22 March 1 99 9. Hornsby a nd Hunter (19 97 ) als o p oi nt o ut that the flrms do not have enough incentives to co op era te under the EC p ol icy . Part of the pro bl em i s a lso due to the fact that the No ti ce c anno t pr ovi de immuni ty from c ivi l pro ceedings. Admi ssio n of a n infri ng ement le ads to a fo rmal Commis sio n De cisi on o n which a n acti on for da mage s ca n b e built, without the plai nti fi havi ng to prov e the infring ement aga in. This pro bl em do es not exi st i n the US, where the co o p erating flrms ca n reso rt to a co ns ent dec ree. 19 create enough incentives for p ost{investigation disclosure of information. It gives only 50{75% reduc- tion of the flnes for co op eration after an investigation has b een undertaken already but only if such an investigation has failed to provide su–cient material for initiating a pro cedure leading to a decision. The US exp erience (where after the 1993 p olicy revision a corp oration is granted leniency after an investigation has b egun provided that \the Division, at the time the corp oration comes in, does not yet have evidence against the company that is likely to result in a sustainable conviction" | p oint B.2.) clearly shows that extension of the leniency program to p ost{investigation amnesty (along with the automatic granting of the amnesty) is a crucial ingredient for success: \...under the old p olicy on average only one corp oration p er year applied for amnesty ," (Spratling (1998, page 2) whereas under the revised p olicy , \Amnesty applications over the past year have b een coming in at the rate of approximately two p er month" (Spratling (1999, page 2). So far, the leniency program of the EC has b een applied to a very reduced numb er of cases, since its intro duction in the end of 1996. There was no case in 1997 and only four in 1998 .We b elieve that granting higher and automatic reductions of flnes and extending the leniency program to after{investigation co op eration would greatly increase the success of this p olicy . References [1] Antitrust Division (1994), Annual Rep ort for Fisc al Y e ar 1994. [2] Beb chuk L. (1984), Litigation and Settlement under Imp erfect Information, Rand Journal of Ec onomics, 15, 404{413. [3] Bingman A., Spratling G., (1995) Criminal Antitrust Enforcement, mimeo. [4] Europ ean Union (1996), Notice on the Non{Imp osition or Reduction of Fines in Cartel Cases, O–cial Journal, v.207, p.4. [5] Europ ean Union (1999), Comp etition Policy Newsletter, No.1, F ebruary . [6] F urse M., (1995), Article 15(2) of Regulation 17: Fines nad the Commission’s Discretion, Eur o- p e an Comp etition L aw Review, p.110. [7] Grossman G., Katz M. (1983), Plea{Bargaining and So cial W elfare, American Economic Review, 7, 749{757. [8] Guerrin M.(1999), Priv ate communication. Electronic message of 5 March 1999. Infor matio n provided by an EC o –cia l, G uerri n (1 99 9). Of these, three rega rded instances of mi no r co op erati on (flrms were given disco unts for not having contested the Commi ssi on’s all ega tions or fo r providing a dditi onal evidenc e which help ed establi shing the facts ). Thes e cas es are \ Al loy surcha rge" , E C Decis ion of 21 Janua ry 1 998 ; \P re-i ns ul ated pip es" , EC Deci sio n o f 21 Octo b er 1 99 8; \ Greek F erri es" , EC Deci sio n o f 9 Decemb er 19 98. The fourth c ase was the \Britis h Sugar" cas e rep orted in the previo us fo otnote, whi ch mi ght b e a di sco ura ging prece dent fo r flrms consideri ng co op erati on with the Co mp etitio n Co mmiss ion. According to Guerri n, i n so me furthe r hal f a dozen current ca ses the Leniency Notic e has b een invoked. No further detail s were gi ven for rea sons of co nfldenti ali ty . 20 [9] Hornsby S., Hunter, J. (1997), New incentives for \whistle{blowing": will the E.C. Commission’s Notice b ear fruit?, Europ ean Comp etition Law Review, 1, 38{41. [10] Kobayashi B. (1992), Deterrents with Multiple Defendants: an Explanation for \Unfair Plea Bargains", Rand Journal of Ec onomics, 22, 507{517. [11] Marshall R., Muerer M., Richard J. (1994), Litigation, Settlement and Collusion, Quarterly Journal of Ec onomics, 1, 211{239. [12] Nalebufi B. (1987), Credible Pre{Tial Negotiation, Rand Journal of Ec onomics, 18, 198{210. [13] Reinganum J. (1988) Plea{Bargaining and Prosecutorial Discretion, Americ an Ec onomic Review, 78, 713{728. [14] Reinganum J., Wilde L. (1987), Settlement, Litigation and the Allo cation of Litigation Costs, Rand Journal of Ec onomics, 17, 557{566. [15] Schweizer U. (1989), Litigation and Settlement under Two{Sided Incomplete Information, Review of Economic Studies, 56, 163{178. [16] Shavell S. (1989), Sharing Information Prior to Settlement or Litigation, Rand Journal of Ec o- nomics, 20, 183{195. [17] Spratling G.R. (1998), The corp orate leniency p olicy: answers to recurring questions, sp eech of the Deputy Assistant Attorney General, presented at the Bar Asso ciation of the District of Columbi a, F ebruary 16, 1999. [18] Spratling G.R. (1999), Making companies an ofier they shouldn’t refuse, sp eech of the Deputy Assistant Attorney General, presented at the ABA Antitrust Section 1999 Spring Meeting, April 1, 1998. [19] V enit J. (1996), EU Comp etition Law | Enforcement and Compliance: An Overview, Antitrust L aw Journal, p.87. Appendix Pro of of Lemma 1 If a flrm reveals, it ge ts a payofi of ƒ =(1 ¡ – ) ¡ R indep e ndentl y of the action chosen by the other flrms. If a flrm do es not reveal any information but at least one flrm do es, then the former flrm receives a payofi of ƒ =(1 ¡ – ) ¡ F . Hence, it is always (weakly) b etter to reveal if the other flrms are exp ected to reveal, which establishes the existence of the \revelation" equilibrium. Finally , if no flrm reveals any information, each flrm receives an exp ected payofi. ƒ ƒ N M p( ¡ F )+ (1 ¡ p) : (15) 1 ¡ – 1 ¡ – 21 If a flrm exp ects the others not to reveal, the b est reply is trivially not to reveal if pF < R.If pF ‚ R, when the other flrms don’t reveal, a flrm prefers not to reveal as well if the payofi ab ove is higher than ƒ =(1 ¡ – ) ¡ F , which simplifles to – ‚ – (p; F ; R). Hence, in this case a \no revelation" equilibrium exists. Moreover, the same inequality implies that the \no revelation" equilibrium gives higher payofis to all flrms than the \revelation" equilibrium. Pro of of Prop osition 2 W e consider the decision to collude or deviate in b oth cases, when flrm will decide to reveal if inves- tigated, and when they will prefer not to co op erate with the AA. † Case 1: –< – . In this case flrms reveal if an investigation is op ened by the AA. Deflne ƒ as the exp ected proflt immediately b efore an investigation is op ened. It is easy to see that: ƒ = fi( ¡ R)+ (1 ¡ fi)(ƒ + – ƒ ) R M R 1 ¡ – from which we obtain: (1 ¡ fi)ƒ + fi( ¡ R) 1¡– ƒ = 1 ¡ – (1 ¡ fi) If a flrm decides to set the collusive price, then its exp ected discounted payofi will b e: ƒ + –fi( ¡ R) 1¡– V =ƒ + – ƒ = CR M R 1 ¡ – (1 ¡ fi) If instead a flrm decides to deviate from the collusive strategy , then its payofi is given by: – ƒ V =ƒ + D D 1 ¡ – Collusion can arise if V ‚ V , that is if the following condition is satisfled: CR D ƒ ¡ ƒ D M – ‚ · – (fi; R): (16) CR (1 ¡ fi)(ƒ ¡ ƒ ) ¡ fiR D N † Case 2: – ‚ – . In this case, flrms anticipate that even if an investigation is started, no flrm will reveal any information. Collusive outcome will b e obtained unless the AA can prove the flrms guilty of collusion. W rite the exp ected proflt immediately b efore knowing if an investigation is op ened as: ƒ ƒ N M ƒ = fi[p( ¡ F )+ (1 ¡ p)( )]+(1 ¡ fi)(ƒ + – ƒ ) NR M NR 1 ¡ – 1 ¡ – W e can then obtain: ƒ ƒ N M fi[p( ¡ F )+ (1 ¡ p)( )] + (1 ¡ fi)ƒ 1¡– 1¡– ƒ = NR 1 ¡ – (1 ¡ fi) If a flrm follows the collusive strategy its exp ected discounted payofi is given by: 22 –fi(1¡p) ƒ (1 + )+ –fip( ¡ F ) 1¡– 1¡– V =ƒ + – ƒ = CN R M NR 1 ¡ – (1 ¡ fi) As b efore, a flrm which deviates obtains a payofi: – ƒ V =ƒ + D D 1 ¡ – The inequality V ‚ V implicitly deflnes the lo cus of p oints – = – (fi; p; F ). CN R D NC NC Pro of of Prop osition 4 W e pro ceed in two steps: flrst we show, for each given outcome NC, CR, CNR, which is the asso ciated optimal p olicy; second, we show the conditions under which a particular outcome is b etter than the others. If a NC outcome is implemented, we can have two cases: either the budget constraint is ab ove t he l ower b oundary of the A region or it is tangent: in the latter case the tangency p oint N C with the fi curve is trivially the optimal solution; if the budget constraint is ab ove that curve, the NC tangency p oint can still b e suggested under a cost saving argument. In this case we set R = F since granting flne discounts would shrink the A region. If a CR outcome is implemented, the welfare NC gain dep ends only on fi, which therefore must b e maximized: we can therefore set R = 0, shifting to the left the p ~ threshold, and setting p =~ p; with p at its lowest level in the A region we can set CR fi = B=w ¡ (w =w )~ p along the budget constraint. Finally if a CNR outcome is chosen, a tangency fi p fi p oint b etween the budget constraint and the indifierence curve in the A region must b e chosen. CN R Consider now the choice among the three outcomes: since W is always dominant for any N C set of p olicy parameters, if the budget constraint is not b elow the fi (p) curve, NC is the optimal NC outcome implemented. The choice b etween a CR and a CNR outcome is more complex, since b oth W and W dep end on the asso ciated p olicy parameters, which, in turn, are difierent at the CN R CR optimal p oints in the two regimes. Supp ose the tangency p oint in the A region b elongs to the CN R subset E : from the deflnition of E , even if the budget constraint in its lower p ortion reaches CN R CN R the A region, it passes through indifierence curves lower than the initial one: hence, picking the CR tangency p oint in the E region and implementing a CNR outcome is the optimal p olicy . On the CN R contrary , if the tangency p oint is in A but not in E , the budget constraint reaches the A CN R CN R CR at a higher indifierence curve, and a CR outcome is optimal. The iso{welfare curves with heterogeneous cartel typ es In the following three Lemmas we identify the iso{welfare curves when the AA faces heterogeneous cartels. Lemma 6 The iso{welfare curves in e ach of the flve re gions have the fol lowing p attern: † in E al l the p olicy c ombination give the same welfare; † in A and D they r eplic ate the shap e of the fi (p) curves; N C † in B they are horizontal; 23 † in C t hey ar e de cr e asing; Pr o of: Since W do es not dep end on the p olicy parameters, all the region corresp ond to the same exp ected welfare. In region A all typ es cho ose CNR. F rom our analysis of the single typ e case we already know that the iso{welfare curves when no typ e colludes have a shap e similar to the fi NC curves (one for each typ e) and in the limit overlap with those. Hence, in region A the indifierence curves replicate the fi curves shap e. In region D high typ es cho ose CNR and lower typ es cho ose NC NC: as long as we move along the fi curve of typ e ƒ , the threshold typ e do es not change and the NC flrst term in W i s unchange d as we ll; moreover, we know that moving along a fi curve we keep the D N C exp ected welfare for typ es cho osing CNR constant. W e conclude that the indifierence curves in region D corresp ond to the fi curves through it. In region B all typ es cho ose CR and the exp ected welfare NC dep ends only on fi, i.e. we have at iso{welfare curves. Finally , in the C region high typ es select CNR and low typ es CR: since W increases when fi is higher (more frequent revelation) as well as when p increases (more efiective prosecution and more typ es induced to reveal), the iso{welfare curve in the C region must b e decreasing. 2 Notice that when no Leniency Program is used, only the regions A, D and E exist, and the result ab ove states that all the curves in A (or D) never pass through another region. Hence, the three relev ant sets of indifierence curves are completely deflned. When R< F all the flve regions A{E exist; the Lemma ab ove deflnes the iso{welfare curves in each region, but now the iso{welfare curves in A (D) eventually continue through region C and B. Hence, we have to carefully check how the iso{welfare curves b ehave moving from one region to the other. Lemma 7 Consider the c ase R<F . The iso{welfare curves p assing through the re gions A{C{B are c ontinous and kinke d at the boundaries of the A and B re gions. The iso{welfar e curves p assing thr ough the re gion D{C{B disc ountinously shift to the right p assing fr om D to C. Pro of: W e start by identifying the indifierence curves that pass through the A{C{B regions. W e already know, b orrowing from the analysis of the single typ e case, that the iso{welfare curve jumps down from A to B, when all typ es cho ose CNR and then CR: however, from the deflnitions of the exp ected welfare we can notice that W tends to W or W as the threshold typ e ƒ tends to ƒ or C A B M ƒ . Hence, the indifierence curves are now continuous; it is easy to check also that they are kinked at the b oundaries of the A and B regions, with the indifierence curve steep er in C than in the other two regions . Consider next the indifierence curves passing through the D{C{B regions: we already established that in D the curves replicate the fi curves shap e, with some typ es cho osing CNR and others NC; NC once moving into the C regions, some typ es still select CNR while others CR. Since the welfare asso ciated to NC is higher than that when CR o ccurs, it must b e that, moving from region D to region C along a iso{welfare curve, less typ es cho ose CNR. That requires a discontinuous jump to the right of the iso{welfare curve once entering in the C region. 2 The concavi ty o r conv e xity of the i ndifiere nce curve in C cannot b e state d i n g eneral, since it dep ends on the distri bution of t yp es g (ƒ ). In what foll ows we consider the case o f concave indi fierence curves, while the extensi on to the co n vex ca se is left to the re ader. 24 Figure 6.a shows the two cases of indifierence curves, one through A{C{B and the other through D{C{B. In the two Lemmas ab ove we have completely characterized the iso{welfare curves when a Leniency Program is intro duced and when it is not. Our next step is to verify when it is convenient to ofier reduced flnes in order to reach a certain exp ected welfare. This exercise correp onds to comparing the iso{welfare curves in the two cases, selecting in the difierent regions the lower one. Lemma 8 When the iso{welfare curve with R =0 p asses thr ough the A{C{B r e gions,it is always optimal to use the leniency Pro gr ams. When the iso{welfare curve with R =0 lies in the D{C{B re gion, the L eniency Pr o grams ar e optimal only in a subset of the C and B re gions. Pro of: Si nc e R = 0 is the more efiective way of inducing CR, we compare the case R = F and R = 0, selecting the lower of the two iso{welfare curves. Since in A and D the iso{welfare curves are the same in b oth regimes, our problem amounts to selecting the lower curve in regions C and B. This can b e done by distinguishing the case in which the indifierence curve with flne reduction passes through the A{C{B region and that in which it lies in the D{C{B areas. Comparing the full and reduced flnes indifierence curves is immediate for the A{C{B case: in the A region they overlap while in the C and B region the iso{welfare curve is lower when R = 0, as shown in flgure 6.a. Hence, the iso{welfare curve through A{C{B is that identifled when the Leniency Program is used. More complex is the comparison of the indifierence curves with and without flne reductions when the former passes through the D{C{B region. In this case, in fact, the iso{welfare curve with flne reductions jumps to the right entering the C region, while with no Leniency Program the indifierence curve, which is the same as b efore in the D area, go es on smo othly in the C region . Hence, entering the C region from the top, the lower indifierence curve is initially the one asso ciated with no flne reduction. It may happ en, as shown in flgure 6.a, that continuing along it, the indifierence curve with flne reductions b ecomes the lower one for a while. Finally , moving further to the right, the indifierence curve with full flnes lies again b elow that with flne reductions. F or higher levels of the exp ected welfare, the indifierence curve with full flnes always dominates that with reduced flnes. Hence, when we consider the indifierence curves for increasing v alue of the exp ected welfare, as long as we are in the A{C{B region we use Leniency Programs, while entering the D{C{B region we adopt reduced flnes only with a subset of p olicy parameters (fi; p), as shown in flgure 6.a. 2 Strictly s p e aking, with no Leniency Prog ra m no C regi on exis ts ; hence we refer to the C reg ion a s thos e p ol icy co m binati ons deflned i n cas e o f flne reduc ti ons. 25 t=0 t=1 t=2 AA F,R a, p f1 D C AA V P D M I a 1-a NI AA f1 P R NR I a 1-a NI f2 R NR R NR f1 P /(1-d)-R P /(1-d)-F AA R NR N N P /(1-d)-R G p 1-p NG P /(1-d)-F P /(1-d) f2 N M R NR R NR P /(1-d)-R P /(1-d)-R AA N N P /(1-d)-R G NG p 1-p P /(1-d)-F P /(1-d) N M Figure 1: The game tree (D: deviation; C: collusion; I: investigation; NI: no investigation; R: reveal; NR: not reveal; G: guilty; NG: not guilty)  E2 E Z 3Z Z 3Z f  6}hi 2@  W4T*i4i?|@M*i @**LU@|L?t  E E2 6}hi 2M  W4T*i4i?|@M*i @**LU@|L?t  f  6}hi ,^*Mh4 TL*U) UL4M?@|L?t  - B f  6}hi e  *|ih?@|i wi?i?U) h*it @?_ 4T*i4i?|@M*i @**LU@|L?t  ( . f  6}hi D  *|T*i |)Tit @?_ 4T*i4i?|@M*i @**LU@|L?t  f  6}hi S@  WtLi*u@hi Uhit | 4*|T*i |)Tit  f  6}hi SM  ,^*Mh4 TL*U) UL4M?@|L?t | 4*|T*i |)Tit

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Published: Jan 1, 1999

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