Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Cecchin, Alekos¹  Pelino, Guglielmo¹ 

[1] Univ Padua, Dept Math Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

关键词: Mean field games;    Finite state space;    Jump Markov processes;    N-person games;    Nash equilibrium;    Master Equation;    Propagation of chaos;    Central Limit Theorem;    Large Deviation Principle;   

DOI  :  10.1016/j.spa.2018.12.002

来源: Elsevier

【 摘 要 】

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled forward-backward ODEs. We exploit the so-called Master Equation, which in this finite-dimensional framework is a first order PDE in the simplex of probability measures, obtaining the convergence of the feedback Nash equilibria, the value functions and the optimal trajectories. The convergence argument requires only the regularity of a solution to the Master Equation. Moreover, we employ the convergence results to prove a Central Limit Theorem and a Large Deviation Principle for the evolution of the N-player empirical measures. The well-posedness and regularity of solution to the Master Equation are also studied, under monotonicity assumptions. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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