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Continuous time finite state space mean-field games


D. Gomes, J. Mohr and R. Sousa, Continuous time finite state space mean-field games, 

Appl. Math. and Opt., Volume 68, Issue 1 (2013), pp 99-143.


D. Gomes, J. Mohr and R. Sousa


Finite state mean-field games, mean field games, mean field limit




In this paper we consider symmetric games where a large number of players can be in any one ofd 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.


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