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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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 nondegenerate. The degenerate case is more delicate and gives rise to counter-examples.

Item Type:	Article
Official URL:	https://projecteuclid.org/info/euclid.aoap
Additional Information:	© 2018 Institute of Mathematical Statistics
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Date Deposited:	05 Oct 2018 13:18
Last Modified:	20 May 2020 00:30
URI:	http://eprints.lse.ac.uk/id/eprint/90362

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