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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 Aggregative game ： ウィキペディア英語版 Aggregative game In game theory, an aggregative game is a game in which every player’s payoff is a function of the player’s own strategy and the aggregate of all players’ strategies. The concept was first proposed by Nobel laureate Reinhard Selten in 1970 who considered the case where the aggregate is the sum of the players' strategies. == Definition == Consider a standard non-cooperative game with ''n'' players, where $S\_i\; \backslash subseteq\; \backslash mathbb$ is the strategy set of player ''i'', $S=S\_1\; \backslash times\; S\_2\; \backslash times\; \backslash ldots\; \backslash times\; S\_n$ is the joint strategy set, and $f\_i:S\; \backslash to\; \backslash mathbb$ is the payoff function of player ''i''. The game is then called an ''aggregative game'' if for each player ''i'' there exists a function $\backslash tilde\_i:S\_i\; \backslash times\; \backslash mathbb\; \backslash to\; \backslash mathbb$ such that for all $s\; \backslash in\; S$: : $f\_i(s)=\backslash tilde\_i\; \backslash left(\; s\_i,\backslash sum\_^n\; s\_j\; \backslash right)$ In words, payoff functions in aggregative games depend on players' ''own strategies'' and the ''aggregate'' $\backslash sum\; s\_j$. As an example, consider the Cournot model where firm ''i'' has payoff/profit function $f\_i(s)=s\_i\; P\backslash left(\backslash sum\; s\_j\backslash right)-C\_i(s\_i)$ (here $P$ and $C\_i$ are, respectively, the inverse demand function and the cost function of firm ''i''). This is an aggregative game since $f\_i(s)=\backslash tilde\_i\backslash left(s\_i,\backslash sum\; s\_j\backslash right)$ where $\backslash tilde\_i(s\_i,X)=s\_i\; P(X)-C\_i(s\_i)$. 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「Aggregative game」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.