Differential games with asymmetric information and without Isaacs’ condition

详细信息    查看全文

• 作者：Rainer Buckdahn ; Marc Quincampoix ; Catherine Rainer…
• 关键词：Zero ; sum differential game ; Asymmetric information ; Isaacs’ condition ; Viscosity solution ; Subdynamic programming principle ; Dual game
• 刊名：International Journal of Game Theory
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：45
• 期：4
• 页码：795-816
• 全文大小：
• 刊物主题：Economic Theory/Quantitative Economics/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Behavioral/Experimental Economics; Operation Research/Decision Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1270
• 卷排序：45

文摘

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.