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About: Game without a value     Goto   Sponge   NotDistinct   Permalink

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In the mathematical theory of games, in particular the study of zero-sum continuous games, not every game has a minimax value. This is the expected value to one of the players when both play a perfect strategy (which is to choose from a particular PDF). This article gives an example of a zero-sum game that has no value. It is due to Sion and Wolfe. The existence of such zero-sum games is interesting because many of the results of game theory become inapplicable if there is no minimax value.