A concept of optimality in differential games†
J. BRADLEY, P. L. Yu · International Journal of Systems Science · 1976
A new concept of optimality in zero-sum, two-player differential games ia 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 surfaco (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 tho classical saddle-point formulation.