On the convergence of finite state mean-field games through Γ-convergence

Rita C. Ferreira; Diogo A. Gomes

doi:10.1016/j.jmaa.2014.02.044

On the convergence of finite state mean-field games through Γ-convergence

Rita C. Ferreira, Diogo A. Gomes

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

Original language	English (US)
Pages (from-to)	211-230
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	418
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.02.044
State	Published - Oct 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: R. Ferreira was supported partially by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through grants SFRH/BPD/81442/2011 and PEst-OE/MAT/UIO297/2011 (CMA).Comes was supported partially by CAMGSD-LARSys through FCT and by grants PTDC/MAT-CAL/0749/2012, UTACMU/MAT/0007/2009, PTDC/MAT/114397/2009, and UTAustin/MAT/0057/2008.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2014.02.044

Cite this

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abstract = "In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. {\textcopyright} 2014 Elsevier Inc.",

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AB - In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

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On the convergence of finite state mean-field games through Γ-convergence

Abstract

Bibliographical note

ASJC Scopus subject areas

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