Continuous time finite state mean field games

Diogo A. Gomes, Joana Mohr, Rafael Rigão Souza

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)99-143
Number of pages45
JournalApplied Mathematics and Optimization
Issue number1
StatePublished - Apr 23 2013

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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