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A group-envy-free division (also known as: coalition-fair division) is a division of a resource among several partners such that every group of partners feel that their allocated share is at least as good as the share of any other group with the same size. The term is used especially in problems of fair division, such as resource allocation and fair cake-cutting. Group-envy-freeness is a very strong fairness requirement: a group-envy-free allocation is both envy-free and Pareto efficient, but the opposite is not true. == Definitions == Consider a set of ''n'' agents. Each agent ''i'' receives a certain allocation ''Ai'' (e.g. a piece of cake or a bundle of resources). Each agent ''i'' has a certain subjective preference relation <''i'' over pieces/bundles (i.e. means that agent ''i'' prefers piece B to piece A). Consider a group X of the agents, with its current allocation . We say that group X prefers a piece B to its current allocation, if there exists a partition of B to the members of X: , such that at least one agent ''i'' prefers his new allocation over his previous allocation (), and no agent prefers his previous allocation over his new allocation. Consider two groups of agents, X and Y, each with the same number ''k'' of agents. We say that group X envies group Y if group X prefers the common allocation of group Y () to its current allocation. An allocation is called group-envy-free if there is no group of agents that envies another group with the same number of agents. 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「Group-envy-free」の詳細全文を読む スポンサード リンク
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