Essential Stationary Equilibria of Mean Field Games with Finite State and Action Space

TL;DR

This paper studies the stability of stationary equilibria in finite state and action mean field games, showing that essential equilibria are prevalent and characterizing their properties.

Contribution

It proves that games with only essential equilibria are generic and provides new characterizations of these equilibria in finite state-action mean field games.

Findings

Essential equilibria are residual in the space of all such games.

Characterizations of essential stationary equilibria are established.

Games with only essential equilibria are prevalent and structurally stable.

Abstract

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of these models are games with finite state and action space, for which recently in Neumann (2020a) a semi-explicit representation of all stationary equilibria has been obtained. In this paper we investigate whether these stationary equilibria are stable against model perturbations. We prove that the set of all games with only essential equilibria is residual and obtain two characterization results for essential stationary equilibria.