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 provide numerical solutions.

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Conference 55th IEEE Conference on Decision and Control, CDC 2016
Huang, M, & Ma, Y. (Yan). (2016). Mean field stochastic games: Monotone costs and threshold policies. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 7105–7110). doi:10.1109/CDC.2016.7799364