Topics in differential games: 1. The existence of saddle points in games of generalized pursuit and evasion. 2. Games with information lags

Xiaojun Qian, Purdue University

Abstract

Two-person zero-sum differential games, where the notions of strategy and payoff are adaptations of those introduced by Berkovitz, are studied. Two principal results are obtained. Berkovitz showed that if the Isaacs condition holds and the data satisfy reasonable hypotheses, differential games of generalized pursuit and evasion have values which are continuous functions of the initial time and state. However, the existence of a saddle point in such games was not obtained. Our first result is that under the same assumptions that Berkovitz used, a saddle point exists. Our second result concerns differential games with information lags. We first extend Berkovitz's notions of strategy and payoff to the games with information lags. It is then shown through an example that if a differential game has a lag, then value of the game does not exist in general. Games of fixed duration with information lags are studied. It is demonstrated that if the Isaacs condition holds, then as the lags tend to zero, the upper and lower values as functions of the lags will tend to the value in the corresponding game with no lags. It is shown that the same results hold also for differential games of generalized pursuit and evasion, as well as games of survival, with lags if certain reasonable conditions on the data and the structure of the terminal set hold.

Degree

Ph.D.

Advisors

Berkovitz, Purdue University.

Subject Area

Mathematics

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