Mean field stochastic games with binary actions: Stationary threshold policies

This paper considers mean field games in a multiagent Markov decision process (MDP) framework. Each player has a continuum state and binary action. We analyze two stationary mean field games with discounted individual costs and long-run average individual costs, respectively. We show existence of a solution to the associated equation system, leading to threshold policies. Uniqueness is obtained under a product form cost and positive externalities.