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- Publisher
- Wiley
- Copyright
- © 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
- ISSN
- 1561-8625
- eISSN
- 1934-6093
- DOI
- 10.1002/asjc.3106
- Publisher site
- See Article on Publisher Site
Abstract
This paper studies large‐population dynamic games involving a linear‐quadratic‐Gaussian (LQG) system with an exponential cost functional. The parameter in the cost functional can describe an investor's risk attitude. In the game, there are a major agent and a population of N$$ N $$ minor agents where N$$ N $$ is very large. The agents in the games are coupled via both their individual stochastic dynamics and their individual cost functions. The mean field methodology yields a set of decentralized controls, which are shown to be an ϵ$$ \epsilon $$‐Nash equilibrium for a finite N$$ N $$ population system where ϵ=O1N$$ \epsilon =O\left(\frac{1}{\sqrt{N}}\right) $$. Numerical results are established to illustrate the impact of the population's collective behaviors and the consistency of the mean field estimation.
Journal
Asian Journal of Control – Wiley
Published: Nov 1, 2023
Keywords: decentralized control; large‐population system; major agent; minor agent; Nash equilibrium; risk‐sensitive