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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Example of a game without a value ： ウィキペディア英語版 Example of a game without a value In game theory, and in particular the study of zero-sum continuous games, it is commonly assumed that a 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.〔 〕 Zero sum games with a finite number of pure strategies are known to have a minimax value (originally proved by John von Neumann) but this is not necessarily the case if the game has an infinite set of strategies. There follows a simple example of a game with no minimax value. 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. ==The game== Players I and II each choose a number, $x$ and $y$ respectively, with $x,y\backslash in()$; the payoff to I is :$K(x,y)=$ \begin -1 & \text x 0 & \text x=y \text y=x+1/2\\ 1 & \text \end (i.e. player II pays $K(x,y)$ to player I;the game is zero-sum). Sometimes player I is referred to as the ''maximizing player'' and player II the ''minimizing player''. If $(x,y)$ is interpreted as a point on the unit square, the figure shows the payoff to player I. Now suppose that player I adopts a mixed strategy: choosing a number from probability density function (pdf) $f$; player II chooses from $g$. Player I seeks to maximize the payoff, player II to minimize the payoff. Note that each player is aware of the other's objective. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Example of a game without a value」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.