Infinite antagonistic games
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In many of the natural sciences (and recently in various social sciences) it is quite common to replace the study of finite sets with a large number of elements by (corresponding) infinite sets. This method allows us to apply the powerful techniques of mathematical analysis to a great variety of problems. Therefore, if we take the case of a game with a large number of strategies for a player then—regardless of whether he or she actually possesses a finite or infinite number of strategies—it is methodologically natural as well as practically useful to assume that the set of strategies for this player is infinite.
KeywordsOptimal Strategy Convex Function Payoff Function Mixed Strategy Pure Strategy
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