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

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