Differential games with information lags

Berkovitz (1985,1986,1988) studied three types of differential games, using a definition of strategy that is an adaptation of that of Friedman (1971) and Karlin and a definition of payoff that is an adaptation of that of Krasovskii and Subbotin (1974). Berkovitz showed that if the Isaacs condition holds and the data satisfy reasonable hypotheses, then the three types of differential games have values which are continuous functions of the initial time and state. He showed that under these hypotheses, games of fixed duration have saddle points, but did not obtain the existence of a saddle point in the other games. The authors present a result that is of interest in its own right and that they use in their study of problems with lags, namely, that if the Isaacs condition holds, then games of generalized pursuit and evasion have saddle points. The authors extend Berkovitz´s definition of differential games to games with information lags and first show through an example that if a differential game of fixed-duration has a lag, then the value of the game does not exist in general