Discrete time, finite state space mean field games

Diogo Gomes*, Joana Mohr, Rafael Rigão Souza

*Corresponding author for this work

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

Abstract

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
EditorsDavid A. Rand, Mauricio Matos Peixoto, Alberto Adrego Pinto
PublisherSpringer Verlag
Pages385-389
Number of pages5
ISBN (Electronic)9783642114557
DOIs
StatePublished - Jan 1 2011
EventInternational conference on dynamical systems and game theory, DYNA 2008 - Braga, Portugal
Duration: Sep 8 2008Sep 12 2008

Publication series

NameSpringer Proceedings in Mathematics
Volume1
ISSN (Print)2190-5614
ISSN (Electronic)2190-5622

Other

OtherInternational conference on dynamical systems and game theory, DYNA 2008
CountryPortugal
CityBraga
Period09/8/0809/12/08

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Discrete time, finite state space mean field games'. Together they form a unique fingerprint.

Cite this