Title: Mean Field Stochastic Games with Binary Action Spaces and Monotone Costs,
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.
By active control, a player can bring its state to a resetting point. All
players are coupled through their cost functions. The structural property of
the individual strategies is characterized in terms of threshold policies when
the mean field game admits a solution. We further introduce a stationary
equation system of the mean field game and analyze uniqueness of its solution
under positive externalities.