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: ''This article is about a part of game theory. For video gaming, see Cooperative gameplay. For the similar feature in some board games, see cooperative board game'' In game theory, a cooperative game is a game where groups of players ("coalitions") may enforce cooperative behaviour, hence the game is a competition between ''coalitions'' of players, rather than between individual players. An example is a coordination game, when players choose the strategies by a consensus decision-making process. Recreational games are rarely cooperative, because they usually lack mechanisms by which coalitions may enforce coordinated behaviour on the members of the coalition. Such mechanisms, however, are abundant in real life situations (e.g. contract law). ==Mathematical definition== A cooperative game is given by specifying a value for every coalition. Formally, the game (coalitional game) consists of a finite set of players , called the ''grand coalition'', and a ''characteristic function'' 〔 denotes the power set of .〕 from the set of all possible coalitions of players to a set of payments that satisfies . The function describes how much collective payoff a set of players can gain by forming a coalition, and the game is sometimes called a ''value game'' or a ''profit game''. The players are assumed to choose which coalitions to form, according to their estimate of the way the payment will be divided among coalition members. Conversely, a cooperative game can also be defined with a characteristic cost function satisfying . In this setting, players must accomplish some task, and the characteristic function represents the cost of a set of players accomplishing the task together. A game of this kind is known as a ''cost game''. Although most cooperative game theory deals with profit games, all concepts can easily be translated to the cost setting. 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「cooperative game」の詳細全文を読む スポンサード リンク
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