Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games

• 成果类型: Article; Early Access
• 署名作者: Cohen, Asaf; Zell, Ethan
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2024.0478
• 发表日期: 2025
• 关键词: mckean-vlasov systems; large deviations; CONVERGENCE; EQUATIONS

摘要

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric n-player games. We consider the finiteprove that any solution to the MFG system gives rise to a (C/ ffififfi state, infinite-horizon problem with ergodic cost. Assuming Markovian strategies, we first Vn)-Nash equilibrium in the n-player game. We follow this result by proving the same is true for the strategy profile derived from the master equation. We conclude the main theoretical portion of the paper by establishing a large deviation principle for empirical measures associated with the asymptotic Nash equilibria. Then, we contrast the asymptotic Nash equilibria using an example. We solve the MFG system directly and numerically solve the ergodic master equation by adapting the deep Galerkin method. We use these results to derive the strategies of the asymptotic Nash equilibria and compare them. Finally, we derive an explicit form for the rate functions in dimension two.