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

• Published in: Stochastic processes and their applications Vol. 129; no. 11; pp. 4510 - 4555
• Main Authors: Cecchin, Alekos, Pelino, Guglielmo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2019
• Subjects: [formula omitted]-person games; Central Limit Theorem; Finite state space; Jump Markov processes; Large Deviation Principle; Master Equation; Mean field games; Nash equilibrium; Propagation of chaos; 60F10; Nash equilibrium; Master Equation; N-person games; 91A10; 93E20; Finite state space; Jump Markov processes; Propagation of chaos; Large Deviation Principle; 60J27; Central Limit Theorem; 60K35; Mean field games; 60F05
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/j.spa.2018.12.002

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,...