标题：Differential games with asymmetric information and without Isaacs' condition
作者：Buckdahn, Rainer; Quincampoix, Marc; Rainer, Catherine; Xu, Yuhong
作者机构：[Buckdahn, Rainer; Quincampoix, Marc; Rainer, Catherine; Xu, Yuhong] Univ Brest, CNRS, UMR 6205, Lab Math, Brest, France.; [Xu, Yuhong] Suzhou Univ, 更多
通讯作者地址：[Quincampoix, M]Univ Brest, CNRS, UMR 6205, Lab Math, Brest, France.
来源：INTERNATIONAL JOURNAL OF GAME THEORY
关键词：Zero-sum differential game; Asymmetric information; Isaacs' condition;; Viscosity solution; Subdynamic programming principle; Dual game
摘要：We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs' condition. The dynamics is an ordinary differential equation parametrized by two controls chosen by the players. Each player has a private information on the payoff of the game, while his opponent knows only the probability distribution on the information of the other player. We show that a suitable definition of random strategies allows to prove the existence of a value in mixed strategies. This value is taken in the sense of the limit of any time discretization, as the mesh of the time partition tends to zero. We characterize it in terms of the unique viscosity solution in some dual sense of a Hamilton-Jacobi-Isaacs equation. Here we do not suppose the Isaacs' condition, which is usually assumed in differential games.