近似EFX分配与序数和有限基数信息
Approximate-EFX Allocations with Ordinal and Limited Cardinal Information
AI总结：
本文研究了在有限信息下实现近似EFX公平分配的算法，探讨了α值与查询数量的权衡，并在特定情况下提供了改进的结果。
摘要：
我们研究了一个离散公平分配问题，其中n个代理对m个物品具有加性估值函数。我们关注众所周知的α-EFX公平性标准，根据该标准，在移除被嫉妒代理 bundle 中的任何物品后，一个代理对另一个代理的嫉妒被乘法地限制在α以内。大多数文献在假定完全了解代理估值函数的情况下研究α-EFX分配。受社会选择中扭曲文献的启发，我们考虑在有限信息下运行的α-EFX算法。特别是，我们假设算法可以访问序数偏好排名，并被允许进行少量查询以获得代理对物品的底层值。我们展示了α值和所需查询数量之间的（近）最优权衡，特别关注常数EFX近似。我们还考虑了两个有趣的特殊情况，即代理数量为常数或物品有两个可能值的情况，并提供了改进的积极结果。
英文摘要：
We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $α$-EFX fairness criterion, according to which the envy of an agent for another agent is bounded multiplicatively by $α$, after the removal of any good from the envied agent's bundle. The vast majority of the literature has studied $α$-EFX allocations under the assumption that full knowledge of the valuation functions of the agents is available. Motivated by the established literature on the distortion in social choice, we instead consider $α$-EFX algorithms that operate under limited information on these functions. In particular, we assume that the algorithm has access to the ordinal preference rankings, and is allowed to make a small number of queries to obtain further access to the underlying values of the agents for the goods. We show (near-optimal) tradeoffs between the values of $α$ and the number of queries required to achieve those, with a particular focus on constant EFX approximations. We also consider two interesting special cases, namely instances with a constant number of agents, or with two possible values, and provide improved positive results.
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