Calculus of Variations and Geometric Measure Theory

C. Jimenez - M. Quincampoix - Y. Xu

Differential games with incomplete information on a continuum of initial positions and without Isaacs condition

created by jimenez on 25 Feb 2015


Accepted Paper

Inserted: 25 feb 2015
Last Updated: 25 feb 2015

Journal: Dynamic games and applications
Year: 2015


This article deals with a two-player zero-sum differential game with infinitely many initial positions and without Isaacs condition. The structure of information is asymmetric: The first player has a private information on the initial position while the second player knows only a probability distribution on the initial position. In the present model, we face two difficulties: First, the incomplete information structure does not reduce to a finite set (as in the famous Aumann-Maschler model for repeated games). Second, the game does not satisfy the Isaacs condition (crucially used in classical approaches to differential games). Therefore, we use tools from optimal transportation theory and stochastic control.