Saddlepoint Optimality in Differential Games.
NAVAL RESEARCH LAB WASHINGTON D C
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A family of two-person zero-sum differential games in which the admissible strategies are Borel measurable is defined, and two types of saddlepoint conditions are introduced as optimality criteria. In one, saddlepoint candidates are compared at each point of the state space with all playable pairs at that point in the other, they are compared only with strategy pairs playable on the entire state space. As a theorem, these two types of optimality are shown to be equivalent for the defined family of games. Also, it is shown that a certain closure property is sufficient for this equivalence. A game having admissible strategies everywhere constant in which the two types of saddlepoint candidates are not equivalent is discussed. Author
- Operations Research