2023/01/17 by Ziteng Cheng, Cheng, Ziteng, Sebastian Jaimungal +1
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Decision-Making and Behavioral Economics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2301.06930
openalex publication_date 2023/01/17 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28
In this paper, we use mean field games (MFGs) to investigate approximations of N-player games (NpGs) with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected utility of total costs), we use an abstract evaluation functional for their performance criteria. Centered around the notion of exploitability, we conduct non-asymptotic analysis on the approximation capability of MFGs from the perspective of state-action distributions without requiring the uniqueness of equilibria. Under suitable assumptions, we first show that scenarios in the NpGs with large N and small average exploitabilities can be well approximated by approximate solutions of MFGs with relatively small exploitabilities. We then show that δ-mean field equilibria can be used to construct ε-equilibria in NpGs. Furthermore, in this general setting, we prove the existence of mean field equilibria. This proof reveals a possible avenue for incorporating penalization for randomized action into MFGs.