先验独立 b-匹配机制的失真
The Distortion of Prior-Independent b-Matching Mechanisms
AI总结：
该研究提出了一种在代理偏好随机生成时具有最优失真和近最优失真间隙的 ordinal 机制，改进了传统最坏情况分析的悲观结果。
摘要：
在需要将 m 个物品分配给 n 个代理的设置中，我们评估了以每个代理的顺序偏好（即对物品从最到最不偏好进行排序）作为输入的机制的性能。评估 ordinal 机制的标准是失真，而大多数关于失真的文献都集中在最坏情况分析上，导致了一些过于悲观的结果。我们相反地评估了机制在代理偏好随机生成时的预期性能的失真。我们首先证明，即使每个代理恰好需要获得一个物品（即 m = n）且每个代理对不同物品的价值是独立同分布地从相同已知分布中抽取的，也没有 ordinal 机制能够达到比 e/(e-1)≈1.582 更好的失真。我们随后通过提出一个 ordinal 机制来补充这一负面结果，该机制即使在每个代理的价值是从未知机制的 agent-specific 分布中抽取的情况下，也能达到最优的失真 e/(e-1)。为了进一步细化我们的分析，我们还优化了失真间隙，即 ordinal 机制在实例上所能达到的最佳失真程度的近似程度，并提出了一种具有近最优失真间隙 1.076 的机制。最后，我们还评估了具有单次通过结构的简单机制的失真和失真间隙。
英文摘要：
In a setting where $m$ items need to be partitioned among $n$ agents, we evaluate the performance of mechanisms that take as input each agent's \emph{ordinal preferences}, i.e., their ranking of the items from most- to least-preferred. The standard measure for evaluating ordinal mechanisms is the \emph{distortion}, and the vast majority of the literature on distortion has focused on worst-case analysis, leading to some overly pessimistic results. We instead evaluate the distortion of mechanisms with respect to their expected performance when the agents' preferences are generated stochastically. We first show that no ordinal mechanism can achieve a distortion better than $e/(e-1)\approx 1.582$, even if each agent needs to receive exactly one item (i.e., $m=n$) and every agent's values for different items are drawn i.i.d.\ from the same known distribution. We then complement this negative result by proposing an ordinal mechanism that achieves the optimal distortion of $e/(e-1)$ even if each agent's values are drawn from an agent-specific distribution that is unknown to the mechanism. To further refine our analysis, we also optimize the \emph{distortion gap}, i.e., the extent to which an ordinal mechanism approximates the optimal distortion possible for the instance at hand, and we propose a mechanism with a near-optimal distortion gap of $1.076$. Finally, we also evaluate the distortion and distortion gap of simple mechanisms that have a one-pass structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
