Continuous time finite state mean field games

Abstract

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 the $N+1$-player problem, which the mean field model attempts to approximate. Our main result is the convergence as $N\to \infty$ 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.

37 pages

References in corpus (2)

• Mean Field Games and Nonlinear Markov Processes
• From infinity to one: The reduction of some mean field games to a global control problem

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