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We consider an n-player symmetric stochastic game with weak interactionbetween the players. Time is continuous and the horizon and the number ofstates are finite. We show that the value function of each of the players canbe approximated by the solution of a partial differential equation called themaster equation. Moreover, we analyze the fluctuations of the empirical measureof the states of the players in the game and show that it is governed by asolution to a stochastic differential equation. Finally, we prove theregularity of the master equation, which is required for the above results.

Analysis of a Finite State Many Player Game Using its Master Equation