### Finite-state mean-field games and the master equation.

Probability Seminar

2nd April 2021, 3:15 pm – 4:15 pm

Online, Zoom

We consider an n-player symmetric stochastic game with weak interactions between N players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated by the solution of a partial differential equation called the master equation. Moreover, we analyze the fluctuations of the empirical measure of the states of the players in the game and show that it is governed by a solution to a stochastic differential equation.

Joint work with Erhan Bayraktar

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