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N-player games and mean field games with absorption

Campi, Luciano and Fischer, Markus (2018) N-player games and mean field games with absorption. Annals of Applied Probability, 28 (4). pp. 2188-2242. ISSN 1050-5164

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Identification Number: 10.1214/17-AAP1354

Abstract

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding N-player games, the evolution of players’ states is described by a system of weakly interacting Itô equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We justify our definition of solution in the usual way, that is, by showing that a solution of the mean field game induces approximate Nash equilibria for the N-player games with approximation error tending to zero as N tends to infinity. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples.

Item Type: Article
Official URL: http://imstat.org/aap/
Additional Information: © 2017 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 27 Sep 2017 14:03
Last Modified: 06 Sep 2019 18:12
URI: http://eprints.lse.ac.uk/id/eprint/84335

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