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

By Alekos Cecchin, Guglielmo Pelino. Stochastic Processes and their Applications, 2017

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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 method 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.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b7e1422e4eee4266ee59f2f48fd9ab97f510a459

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Citations in the corpus

Applications of Mean Field Games in financial engineering and economic theory (2020, methodology): “The probabilistic approach to finite state mean field games is advocated by Cecchin and Fischer in [33], Bayraktar and Cohen derived the equivalent of the master equation in [10], and the convergence problem is studied in [42] by Doncel, Gast and Gaujal, and in [34] by Cecchin and Pelino.”