两全其美的公平性与帕累托最优
Best-of-Both-Worlds Fairness and Pareto Optimality
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中文总结 AI 辅助
该研究针对不可分物品公平分配问题，提出构造满足无嫉妒及EFX、帕累托最优的确定性分配彩票的方法，证明两主体时可行，三主体四物品时可能不存在符合要求的事前无嫉妒彩票。
中文摘要 AI 辅助
我们考虑在具有非负加法估值的主体间对不可分物品进行公平分配，目标是构造一个确定性分配的彩票，其诱导的分数分配是无嫉妒的，同时每个实现的分配是无嫉妒至多一件物品（EFX）且帕累托最优的。我们证明该情况对两个主体总是可行，还证明存在更强结果：对确定性分配的彩票，其诱导的分数分配无嫉妒，每个实现的分配是EFX且帕累托最优。对于非负整数加法估值，此类彩票可在伪多项式时间内计算。我们还证明，对于三个主体和四件物品，可能不存在可由同时为EFX且帕累托最优的分配支撑的事前无嫉妒彩票。
英文摘要
We consider fair allocation of indivisible items among agents with non-negative and additive valuations. The goal is to construct a lottery over deterministic allocations whose induced fractional allocation is envy-free, while every realised allocation is envy-free up to one item and Pareto optimal. We show that this is always possible for two agents. We then prove a stronger result that there always exists a lottery over deterministic allocations whose induced fractional allocation is envy-free, while every realised allocation is envy-free up each one item (EFX) and Pareto optimal. For non-negative integral additive valuations, such a lottery can be computed in pseudo-polynomial time. We also prove that for three agents and four items, there may be no ex-ante envy-free lottery that can be supported on allocations that are simultaneously EFX and Pareto optimal.
