Zero-Sum Mean-Field Dynkin Games: Characterization and Convergence
将经典零和Dynkin博弈扩展到支付过程依赖博弈值及其概率律的平均场情形，证明了博弈存在值和鞍点的条件，并用一类平均场型双反射倒向随机微分方程刻画了博弈值，还给出了弱相互作用系统的适定性和混沌传播结果。
We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish sufficient conditions under which such a game admits a value and a saddle point. Furthermore, we provide a characterization of the value of the game in terms of a specific class of doubly reflected backward stochastic differential equations of mean-field type, for which we derive an existence and uniqueness result. We then introduce a corresponding system of weakly interacting zero-sum Dynkin games and show its well-posedness. Finally, we provide a propagation of chaos result for the value of the zero-sum mean-field Dynkin game.