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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 Correlated equilibrium ： ウィキペディア英語版 Correlated equilibrium In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann (1974). The idea is that each player chooses his/her action according to his/her observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from the recommended strategy (assuming the others don't deviate), the distribution is called a correlated equilibrium. ==Formal definition== An $N$-player strategic game $\backslash displaystyle\; (N,A\_i,u\_i)$ is characterized by an action set $A\_i$ and utility function $u\_i$ for each player $i$. When player $i$ chooses strategy $a\_i\; \backslash in\; A\_i$ and the remaining players choose a strategy profile described by the $N-1$-tuple $a\_$, then player $i$'s utility is $\backslash displaystyle\; u\_i(a\_i,a\_)$. A ''strategy modification'' for player $i$ is a function $\backslash phi\backslash colon\; A\_i\; \backslash to\; A\_i$. That is, $\backslash phi$ tells player $i$ to modify his behavior by playing action $\backslash phi(a\_i)$ when instructed to play $a\_i$. Let $(\backslash Omega,\; \backslash pi)$ be a countable probability space. For each player $i$, let $P\_i$ be his information partition, $q\_i$ be $i$'s posterior and let $s\_i\backslash colon\backslash Omega\backslash rightarrow\; A\_i$, assigning the same value to states in the same cell of $i$'s information partition. Then $((\backslash Omega,\; \backslash pi),P\_i)$ is a correlated equilibrium of the strategic game $(N,A\_i,u\_i)$ if for every player $i$ and for every strategy modification $\backslash phi$: :$\backslash sum\_\; q\_i(\backslash omega)u\_i(s\_i,\; s\_)\; \backslash geq\; \backslash sum\_\; q\_i(\backslash omega)u\_i(\backslash phi(s\_i),\; s\_)$ In other words, $((\backslash Omega,\; \backslash pi),P\_i)$ is a correlated equilibrium if no player can improve his or her expected utility via a strategy modification. 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「Correlated equilibrium」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.