标题：ZERO-SUM AND NONZERO-SUM DIFFERENTIAL GAMES WITHOUT ISAACS CONDITION
作者：Li, Juan; Li, Wenqiang
作者机构：[Li, Juan; Li, Wenqiang] Shandong Univ, Sch Math & Stat, Weihai 264209, Weihai, Peoples R China.; [Li, Wenqiang] Yantai Univ, Sch Math & Informat Sc 更多
通讯作者地址：[Li, J]Shandong Univ, Sch Math & Stat, Weihai 264209, Weihai, Peoples R China.
来源：ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
关键词：Zero-sum and nonzero-sum differential game; asymmetric information;; Isaacs condition; Nash equilibrium payoffs; Fenchel transformation
摘要：In this paper we study differential games without Isaacs condition. The objective is to investigate on one hand zero-sum games with asymmetric information on the pay-off, and on the other hand, for the case of symmetric information but now for a non-zero sum differential game, the existence of a Nash equilibrium pay-off. Our results extend those by Buckdahn, Cardaliaguet and Rainer [SIAM J. Control Optim. 43 (2004) 624-642], to the case without Isaacs condition. To overcome the absence of Isaacs condition, randomization of the non-anticipative strategies with delay of the both players are considered. They differ from those in Buckdahn, Quincampoix, Rainer and Xu [Int. J. Game Theory 45 (2016) 795-816]. Unlike in [Int. J. Game Theory 45 (2016) 795-816], our definition of NAD strategies for a game over the time interval [t, T] (0 <= t <= T) guarantees that a randomized strategy along a partition pi of [0, T] remains a randomized NAD strategy with respect to any finer partition pi' (pi subset of pi'). This allows to study the limit behavior of upper and lower value functions defined for games in which the both players use also different partitions.