Envy-freeness

Envy-freeness is a criterion of fair division. An envy-free division is a division in which every partner feels that his or her allocated share is at least as good as any other share.

A resource is divided among several partners such that every partner ${\displaystyle i}$ receives a share ${\displaystyle X_{i}}$. Every partner ${\displaystyle i}$ has a subjective preference relation ${\displaystyle \succeq _{i}}$ over different possible shares. The division is called envy-free if for all ${\displaystyle i}$ and ${\displaystyle j}$:

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