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Competitive equilibria in matching markets with budgets

Competitive equilibria in matching markets with budgets Competitive Equilibria in Matching Markets with Budgets NING CHEN Nanyang Technological University, Singapore and XIAOTIE DENG City University of Hong Kong, Hong Kong and ARPITA GHOSH Yahoo! Research, Santa Clara, CA, USA 1. INTRODUCTION Consider a market with n unit demand buyers and m sellers, each selling one unit of an indivisible good. The buyers specify their preferences over items via utility functions uij (pj ), which is the utility of buyer i for item j when its price is pj . So far, this is the classic Shapley-Shubik assignment model [Shapley and Shubik 1971] which captures a variety of matching markets including housing markets and ad auctions [Edelman et al. 2007], except for the extension to general utility functions instead of the quasi-linear utilities in the original model. Shapley and Shubik show that a competitive equilibrium always exists in their model, and later work [Crawford and Knoer 1981, Quinnzi 1984, Gale 1984] shows that a competitive equilibrium must also exist for the model with general utility functions uij ( ), provided these uij ( ) are strictly decreasing and continuous everywhere. Now suppose we extend the assignment model with an extra budget constraint: a buyer i can http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Competitive equilibria in matching markets with budgets

Chen, Ning; Deng, Xiaotie; Ghosh, Arpita
ACM SIGecom Exchanges , Volume 9 (1) – Jun 1, 2010
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Publisher
Association for Computing Machinery
Copyright
Copyright © 2010 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/1980534.1980539
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Abstract

Competitive Equilibria in Matching Markets with Budgets NING CHEN Nanyang Technological University, Singapore and XIAOTIE DENG City University of Hong Kong, Hong Kong and ARPITA GHOSH Yahoo! Research, Santa Clara, CA, USA 1. INTRODUCTION Consider a market with n unit demand buyers and m sellers, each selling one unit of an indivisible good. The buyers specify their preferences over items via utility functions uij (pj ), which is the utility of buyer i for item j when its price is pj . So far, this is the classic Shapley-Shubik assignment model [Shapley and Shubik 1971] which captures a variety of matching markets including housing markets and ad auctions [Edelman et al. 2007], except for the extension to general utility functions instead of the quasi-linear utilities in the original model. Shapley and Shubik show that a competitive equilibrium always exists in their model, and later work [Crawford and Knoer 1981, Quinnzi 1984, Gale 1984] shows that a competitive equilibrium must also exist for the model with general utility functions uij ( ), provided these uij ( ) are strictly decreasing and continuous everywhere. Now suppose we extend the assignment model with an extra budget constraint: a buyer i can

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ACM SIGecom Exchanges – Association for Computing Machinery

Published: Jun 1, 2010

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