SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 1795-1821, January 2020.
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game. We place ourselves in the framework of relaxed optimal stopping, which amounts to looking for the optimal occupation measure of the stopper rather than the optimal stopping time. This framework allows us to prove the existence of a relaxed Nash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions. Further, we prove a rigorous relation between relaxed Nash equilibria and the notion of mixed solutions introduced in earlier works on the subject and provide a criterion under which the optimal strategies are pure strategies, that is, behave in a similar way to stopping times. Finally, we present a numerical method for computing the equilibrium in the case of potential games and show its convergence.

中文翻译：

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最优停止的均值博弈：一种放松的求解方法

SIAM控制与优化杂志，第58卷，第4期，第1795-1821页，2020年1月。
我们考虑平均场博弈，其中每个代理通过根据仍存在于游戏中的代理状态过程的密度来解决具有奖励函数的最优停止问题，从而确定退出游戏的最佳时间。我们将自己置于放松的最佳停止框架中，这相当于寻找最佳的制动塞占用量，而不是最佳的制动时间。该框架使我们能够证明在温和假设下存在松弛的纳什均衡以及代表代理的关联值的唯一性。此外，我们证明了松弛Nash均衡与早先对此主题引入的混合解的概念之间的严格关系，并提供了一个标准，其中最佳策略是纯策略，即 行为与停止时间类似。最后，我们提出了一种在潜在博弈情况下计算均衡的数值方法，并证明了其收敛性。