In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: D. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT-CAL/0749/2012, UTA-CMU/MAT/0007/2009 PTDC/MAT/114397/2009, UTAustin-MAT/0057/2008, and by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. R.R.S. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. J.M. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09.
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics