Mean Field Games and Nonlinear Markov Processes

• DOI: 10.48550/arxiv.1112.3744
• Publication Date: 2011-01-01
• Authors: Kolokoltsov, Vass...; Li, Jiajie; Yang, Wei
• Keywords: Probability (math.PR); FOS: Mathematics; 0101 mathematics; 01 natural sciences; Mathematics - Probability

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 L��vy-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.<br/>60 pages, results reported at SIAM (Contol) July 2011, Vienna ECCS'11 Sep. 2011, Warwick (Topics in Control) Dec. 2011, 2nd version just improves wording and formulations in many places<br/>