Repeated Games and Qualitative Differential Games: Approachability and Comparison of Strategies

We study the notion of approachability in a repeated game with vector payoffs from a new point of view using techniques recently developed for qualitative differential games. Namely, we relate the sufficient condition for approachability (B-set) to the notion of discriminating domain for a suitably chosen differential game. The other goal of the present article is to obtain a new precise link between the strategies in the differential game and in the repeated game preserving approachability properties.