Discrete time, finite state space mean field games

Diogo A. Gomes; Joana Mohr; Rafael Rigão Souza

doi:10.1007/978-3-642-11456-4_26

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 proceeding › Conference contribution › peer-review

2 Scopus citations

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 language	English (US)
Title of host publication	Dynamics, Games and Science I
Subtitle of host publication	DYNA 2008, in Honor of Mauricio Peixoto and David Rand
Editors	Mauricio Matos Peixoto, David A. Rand, Alberto Adrego Pinto
Publisher	Springer Verlag
Pages	385-389
Number of pages	5
ISBN (Electronic)	9783642114557
DOIs	https://doi.org/10.1007/978-3-642-11456-4_26
State	Published - 2011
Externally published	Yes
Event	International conference on dynamical systems and game theory, DYNA 2008 - Braga, Portugal Duration: Sep 8 2008 → Sep 12 2008

Publication series

Name	Springer Proceedings in Mathematics
Volume	1
ISSN (Print)	2190-5614
ISSN (Electronic)	2190-5622

Other

Other	International conference on dynamical systems and game theory, DYNA 2008
Country/Territory	Portugal
City	Braga
Period	09/8/08 → 09/12/08

ASJC Scopus subject areas

General Mathematics
Statistics, Probability and Uncertainty

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10.1007/978-3-642-11456-4_26

Cite this

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title = "Discrete time, finite state space mean field games",

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.",

author = "Gomes, {Diogo A.} and Joana Mohr and Souza, {Rafael Rig{\~a}o}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2011.; International conference on dynamical systems and game theory, DYNA 2008 ; Conference date: 08-09-2008 Through 12-09-2008",

year = "2011",

doi = "10.1007/978-3-642-11456-4_26",

language = "English (US)",

series = "Springer Proceedings in Mathematics",

publisher = "Springer Verlag",

pages = "385--389",

editor = "Peixoto, {Mauricio Matos} and Rand, {David A.} and Pinto, {Alberto Adrego}",

booktitle = "Dynamics, Games and Science I",

address = "Germany",

}

Gomes, DA, Mohr, J & Souza, RR 2011, Discrete time, finite state space mean field games. in MM Peixoto, DA Rand & AA Pinto (eds), Dynamics, Games and Science I: DYNA 2008, in Honor of Mauricio Peixoto and David Rand. Springer Proceedings in Mathematics, vol. 1, Springer Verlag, pp. 385-389, International conference on dynamical systems and game theory, DYNA 2008, Braga, Portugal, 09/8/08. https://doi.org/10.1007/978-3-642-11456-4_26

Discrete time, finite state space mean field games. / Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão.
Dynamics, Games and Science I: DYNA 2008, in Honor of Mauricio Peixoto and David Rand. ed. / Mauricio Matos Peixoto; David A. Rand; Alberto Adrego Pinto. Springer Verlag, 2011. p. 385-389 (Springer Proceedings in Mathematics; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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Discrete time, finite state space mean field games

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