On saddle-point optimality in differential games
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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 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.
Key WordsDifferential games playability saddle-point optimality
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- 1.Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965 (p. 38).Google Scholar
- 2.Berkovitz, L. D.,Łectures on Differential Games, Necessary Conditions for Optimal Strategies in a Class of Differential Games and Control Problems, SIAM Journal on Control, Vol. 5, No. 1, 1967.Google Scholar
- 3.Berkovitz, L. D.,Differential Games and Related Topics, Edited by H. W. Kuhn and G. P. Szego, North-Holland Publishing Company, Amsterdam, Holland, 1971 (p. 3).Google Scholar
- 4.Stalford, H.,Sufficiency Conditions in Optimal Control and Differential Games, University of California, Berkeley, California, Operations Research Center, Report No. ORC-70-13, 1970.Google Scholar
- 5.Stalford, H., andLeitmann, G.,Sufficient Conditions for Optimality in Two-Person Zero-Sum Differential Games with State and Strategy Constraints, Journal of Mathematical Analysis and Applications, Vol. 33, No. 3, 1971.Google Scholar
- 6.Varaiya, P., andLin, J.,Existence of Saddle Points in Differential Games, SIAM Journal on Control, Vol. 7, No. 1, 1969.Google Scholar
- 7.Stalford, H., andLeitmann, G.,On the Equivalence of Two Criteria for Optimal Closed-Loop Control, Ricerche di Automatica, Vol. 4, Nos. 2–3, 1973.Google Scholar