  Stochastic games provide a framework for interactions among multiple agents
and enable a myriad of applications. In these games, agents decide on actions
simultaneously, the state of every agent moves to the next state, and each
agent receives a reward. However, finding an equilibrium (if exists) in this
game is often difficult when the number of agents becomes large. This paper
focuses on finding a mean-field equilibrium (MFE) in an action coupled
stochastic game setting in an episodic framework. It is assumed that the impact
of the other agents' can be assumed by the empirical distribution of the mean
of the actions. All agents know the action distribution and employ lower-myopic
best response dynamics to choose the optimal oblivious strategy. This paper
proposes a posterior sampling based approach for reinforcement learning in the
mean-field game, where each agent samples a transition probability from the
previous transitions. We show that the policy and action distributions converge
to the optimal oblivious strategy and the limiting distribution, respectively,
which constitute an MFE.
