Existence of value in differential games with fixed time duration

A differential game of prescribed duration with general-type phase constraints is investigated. The existence of a value in the Varaiya-Lin sense and an optimal strategy for one of the players is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. These results are next widened on more general games, examined earlier by Varaiya.The author wishes to express his thanks to an anonymous reviewer for his many valuable comments.