Mixed Strategies for Deterministic Differential Games

This paper considers mixed strategies for two player, zero sum differential games on a finite time interval. Motivated by the classical result in static games that ensures the existence of a saddle point when mixed strategies are allowed for both players, we extend those ideas to differential games, introducing a Law of Large Numbers game, for which the value function coincides with the limit of discrete time Markov games. Finally, of particular interest is the class of strategies called approximately optimal Markov strategies, which are studied in the last part.