On saddle-point optimality in differential games |
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Authors: | H L Stalford G Leitmann |
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Institution: | (1) Radar Division, Naval Research Laboratory, Washington, DC;(2) University of California, Berkeley, California |
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Abstract: | A family of two-person, zero-sum differential games in which the admissible strategies are Borel measurable is defined, and two types of saddle-point conditions are introduced as optimality criteria. In one, saddle-point candidates are compared at each point of the state space with all playable pairs at that point; and, 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 saddle-point candidates are not equivalent, is discussed.This paper is based on research supported by ONR. |
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Keywords: | Differential games playability saddle-point optimality |
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