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- W1618063691 abstract "Abstract A natural extension of Isaac's formulation [1] leads to differential games which are described by differential equations with aftereffect and as regards information are determined by information on the whole prehistory of the game. In this paper relating closely to the investigations in [2 – 10], the emphasis is on the proof of the existence theorem for the value of the differential game in such an extended formulation. We examine a differential game of prescribed duration with a pay-off given in the form of a functional on the game's trajectory. The differential game is approximated by a certain family of multistage games. We consider two sequences (minimax and maximin) comprised of the minimax and the maximin values of the payoff in the multistage games. Conditions are obtained under whose fulfillment these sequences converge and their limits are equal. The proof of the convergence of the minimax and maximin sequences is carried out by a scheme suggested by Fleming [2], The proof of the equality of the limits of these sequences is based on the results of Krasovskii and Subbotin [8, 9]." @default.
- W1618063691 created "2016-06-24" @default.
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- W1618063691 date "1972-01-01" @default.
- W1618063691 modified "2023-09-25" @default.
- W1618063691 title "On the existence of the value of a differential game of specified duration" @default.
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- W1618063691 doi "https://doi.org/10.1016/0021-8928(72)90155-4" @default.
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