Preprintgreen2011

Mean Field Games and Nonlinear Markov Processes

Vassili Nikitich Kolokoltsov · Jiajie Li · Wei Qing Yang

67 citations0/0 files storedarXiv (Cornell University)

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Stochastic processes and financial applications Game Theory and Applications Stochastic processes and statistical mechanics

Abstract

In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of Lévy-Khintchine type (with variable coefficients). We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents.

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References

1975Reexamination of the perfectness concept for equilibrium points in extensive games 2005Controlled Markov Processes and Viscosity Solutions 2007Mean field games 2006Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle 2007Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria 2010Mean Field Games and Applications 1980Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives 2010A Maximum Principle for SDEs of Mean-Field Type

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