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arXiv · 1203.3173

Continuous time finite state mean field games

Diogo A. Gomes·Joana Mohr·Rafael R. Souza
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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.

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Diogo A. Gomes, Joana Mohr, Rafael R. Souza. 2012-03-14. Continuous time finite state mean field games. https://doi.org/10.1007/s00245-013-9202-8

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