A Concept of Optimality in Differential Games.
TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES
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A new concept of optimality in zero-sum, two-play differential games is presented and studied. This concept consists of a local semipermeable condition and a global reprisal condition. The latter is introduced to overcome certain difficulties which arise in differential games in which there exist strategy pairs which yield paths which do not meet the terminal surface or set. It is shown that when specified conditions are satisfied, distinct optimal strategies yield the same value function, optimal strategies are interchangeable, and the resulting value function satisfies Isaacs equation. Furthermore, in games of finite duration or other all-terminating games, this concept reduces to the classical saddle-point formulation. Author
- Operations Research