ANALYSIS OF A FINITE STATE MANY PLAYER GAME USING ITS MASTER EQUATION
ANALYSIS OF A FINITE STATE MANY PLAYER GAME USING ITS MASTER EQUATION
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DOI：
10.1137/17m113887x
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发表时间：
2018-01-01
影响因子：
2.2
通讯作者：
Cohen, Asaf
中科院分区：
文献类型：
--
作者：
Bayraktar, Erhan;Cohen, Asaf
本文研究了一个局中人之间具有弱相互作用的n个局中人对称随机对策。时间是连续的，视界和状态的数量是有限的。我们表明，每个球员的价值函数可以近似的偏微分方程的主方程的解决方案。此外，我们分析了波动的经验措施的国家的球员在游戏中，并表明，它是由一个随机微分方程的解决方案。最后，我们证明了主方程的正则性，这是上述结果所必需的。
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.