Zero-sum and nonzero-sum differential games without Isaacs condition
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1217-1252.

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] (0tT) guarantees that a randomized strategy along a partition π of [0,T] remains a randomized NAD strategy with respect to any finer partition π' (ππ'). 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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016044
Classification : 49N70, 49L25, 91A23, 60H10
Mots clés : Zero-sum and nonzero-sum differential game, asymmetric information, Isaacs condition, Nash equilibrium payoffs, Fenchel transformation
Li, Juan 1 ; Li, Wenqiang 1, 2

1 School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P.R. China.
2 School of Mathematics and Information Sciences, Yantai University, Yantai 264005, P.R. China.
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Li, Juan; Li, Wenqiang. Zero-sum and nonzero-sum differential games without Isaacs condition. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1217-1252. doi : 10.1051/cocv/2016044. http://www.numdam.org/articles/10.1051/cocv/2016044/

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