Binary Mean Field Stochastic Games: Stationary Equilibria and Comparative Statics

TL;DR

This paper studies binary action mean field games with a continuum of states, establishing existence and uniqueness of stationary equilibria, and analyzing how effort costs influence equilibrium outcomes.

Contribution

It introduces a novel analysis of stationary equilibria in binary action mean field games, including existence, uniqueness, and comparative statics under externality conditions.

Findings

Existence of stationary equilibrium proven.

Uniqueness established under positive externality.

Effort costs significantly affect equilibrium characteristics.

Abstract

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an infinite horizon discounted individual cost, we show existence of a stationary equilibrium, and prove its uniqueness under a positive externality condition. We further analyze comparative statics of the stationary equilibrium by quantitatively determining the impact of the effort cost.