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April 2017 On the connection between symmetric $N$-player games and mean field games
Markus Fischer
Ann. Appl. Probab. 27(2): 757-810 (April 2017). DOI: 10.1214/16-AAP1215

Abstract

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to \infty $. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate Nash equilibria for the corresponding $N$-player games. The opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean field game? In this direction, rigorous results are mostly available for stationary problems with ergodic costs. Here, we identify limit points of sequences of certain approximate Nash equilibria as solutions to mean field games for problems with Itô-type dynamics and costs over a finite time horizon. Limits are studied through weak convergence of associated normalized occupation measures and identified using a probabilistic notion of solution for mean field games.

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Markus Fischer. "On the connection between symmetric $N$-player games and mean field games." Ann. Appl. Probab. 27 (2) 757 - 810, April 2017. https://doi.org/10.1214/16-AAP1215

Information

Received: 1 May 2014; Revised: 1 April 2016; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1375.91009
MathSciNet: MR3655853
Digital Object Identifier: 10.1214/16-AAP1215

Subjects:
Primary: 60K35, 91A06
Secondary: 60B10, 93E20

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 2017
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