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The Bondareva–Shapley theorem, in game theory, describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game. Specifically, the game's core is non-empty if and only if the game is ''balanced''. The Bondareva–Shapley theorem implies that market games and convex games have non-empty cores. The theorem was formulated independently by Olga Bondareva and Lloyd Shapley in the 1960s. == Theorem == Let the pair be a cooperative game, where is the set of players and where the ''value function'' is defined on 's power set (the set of all subsets of ). The core of is non-empty if and only if for every function where the following condition holds: : 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「Bondareva–Shapley theorem」の詳細全文を読む スポンサード リンク
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