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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 Helly metric ： ウィキペディア英語版 Helly metric In game theory, the Helly metric is used to assess the distance between two strategies. It is named for Eduard Helly. Consider a game $\backslash Gamma=\backslash left\backslash langle\backslash mathfrak,\backslash mathfrak,H\backslash right\backslash rangle$, between player I and II. Here, $\backslash mathfrak$ and $\backslash mathfrak$ are the sets of pure strategies for players I and II respectively; and $H=H(\backslash cdot,\backslash cdot)$ is the payoff function. (in other words, if player I plays $x\backslash in\backslash mathfrak$ and player II plays $y\backslash in\backslash mathfrak$, then player I pays $H(x,y)$ to player II). The Helly metric $\backslash rho(x\_1,x\_2)$ is defined as :$$ \rho(x_1,x_2)=\sup_}\left| H(x,y_1)-H(x,y_2)\right|. Note that $\backslash Gamma$ thus defines ''two'' Helly metrics: one for each player's strategy space. ==Conditional compactness== Notation (definition of an $\backslash epsilon$-net). A set $X\_\backslash epsilon$ is an $\backslash epsilon$-net in the space $X$ with metric $\backslash rho$ if for any $x\backslash in\; X$ there exists $x\_\backslash epsilon\backslash in\; X\_\backslash epsilon$ with . A metric space $P$ is conditionally compact if for any $\backslash epsilon>0$ there exists a ''finite'' $\backslash epsilon$-net in $P$. A game that is conditionally compact in the Helly metric has an $\backslash epsilon$-optimal strategy for any $\backslash epsilon>0$. 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「Helly metric」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.