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Envy-freeness : ウィキペディア英語版
Envy-freeness
Envy-freeness is a criterion of fair division. An envy-free division is a division in which every partner feels that his allocated share is at least as good as any other share.
== Definitions ==
A resource is divided among several partners such that every partner i receives a share X_i. Every partner i has a subjective preference relation \succeq_i over different possible shares. The division is called ''envy-free'' if for all i and j:
:::X_i \succeq_i X_j
If the preference of the agents are represented by a value functions V_i, then this definition is equivalent to:
:::V_i(X_i) \geq V_i(X_j)
Put another way: we say that agent i ''envies'' agent j if i prefers the piece of j over his own piece, i.e.:
:::X_i \prec_i X_j
:::V_i(X_i) < V_i(X_j)
A division is called envy-free if no agent envies another agent.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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