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Analysis of a finite state many player game using its master equation. (English) Zbl 1416.91013

Summary: We consider an \(n\)-player symmetric stochastic game with weak interactions between the 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. Finally, we prove the regularity of the master equation, which is required for the above results.

MSC:

91A06 \(n\)-person games, \(n>2\)
91A15 Stochastic games, stochastic differential games
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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