Discrete time, finite state space mean field games

Diogo A. Gomes*, Joana Mohr, Rafael Rigão Souza

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


In this paper we report on some recent results for mean field models in discrete time with a finite number of states. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality criteria. The mean field approach for optimal control and differential games (continuous state and time) was introduced by Lasry and Lions (C. R. Math. Acad. Sci. Paris, 343(9):619–625, 2006; 343(10):679–684, 2006; Jpn. J. Math., 2(1):229–260, 2007). The discrete time, finite state space setting is motivated both by its independent interest as well as by numerical analysis questions which appear in the discretization of the problems introduced by Lasry and Lions. We address existence, uniqueness and exponential convergence to equilibrium results.

Original languageEnglish (US)
Title of host publicationDynamics, Games and Science I
Subtitle of host publicationDYNA 2008, in Honor of Mauricio Peixoto and David Rand
EditorsMauricio Matos Peixoto, David A. Rand, Alberto Adrego Pinto
PublisherSpringer Verlag
Number of pages5
ISBN (Electronic)9783642114557
StatePublished - 2011
Externally publishedYes
EventInternational conference on dynamical systems and game theory, DYNA 2008 - Braga, Portugal
Duration: Sep 8 2008Sep 12 2008

Publication series

NameSpringer Proceedings in Mathematics
ISSN (Print)2190-5614
ISSN (Electronic)2190-5622


OtherInternational conference on dynamical systems and game theory, DYNA 2008

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2011.

ASJC Scopus subject areas

  • General Mathematics
  • Statistics, Probability and Uncertainty


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