发表机构
Adelaide University（阿德莱德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对公共项目VCG再分配机制，移除有界精度假设，构造了适用于[0,1]区间实类型的确定性匿名策略防卫无赤字机制，通过复分析证明其最坏情况效率比为1-O(1/log log n)。
AI 中文摘要
我们研究公共项目问题的最坏情况VCG再分配机制设计，其中n个智能体决定是否建造非排他性公共项目，设计者选择一个Groves项，在不出现赤字的前提下返还尽可能多的VCG支付。目标是最坏情况效率比，即智能体总效用与最优总效用的最坏情况比值。已有研究表明，仅在有界精度假设下，即所有类型为具有共同有界分母的有理数，该比值可随n增大趋近于1。该假设比表面上更严格：它将困难的偏好配置限制为除有界数量智能体外其余均报告0，且报告0的智能体完全知晓总情况。若无该假设，已知的最优保证趋近于1/2。我们移除该假设，针对[0,1]区间内任意实类型，构造了一个确定性、匿名、策略防卫且无赤字的机制，其最坏情况效率比为1-O(1/log log n)。该构造通过以下方式估计报告总额低于项目成本的缺口：用重采样得到的报告填充每个智能体的缺失报告，再估计该估计的误差，接着估计误差的误差，依此类推。经过m轮后，总误差最多为1/(H_m)乘以平均报告，其中H_m为第m个调和数。该界限的证明是本文核心，且与支付相关结果通常不同，它使用复分析：缺口函数的三角表示结合上半平面有界解析函数的Poisson-Jensen不等式。
英文摘要
We study worst-case VCG redistribution mechanism design for the public project problem, where n agents decide whether to build a non-excludable public project and the designer chooses a Groves term that returns as much of the VCG payment as possible without running a deficit. The objective is the worst-case efficiency ratio, the worst-case ratio between the agents' total utility and the first-best total utility. Prior work showed that this ratio can approach 1 as n grows only under a bounded precision assumption, that all types are rational numbers with a common bounded denominator. The assumption is stronger than it looks: it confines the difficult profiles to those in which all but a bounded number of agents report zero, and an agent who reports zero knows the total exactly. Without it, the best known guarantee tends to 1/2. We remove the assumption. We construct a deterministic, anonymous, strategy-proof, and non-deficit mechanism for arbitrary real types in [0,1] whose worst-case efficiency ratio is 1-O(1/log log n). The construction estimates the shortfall of the reported total below the project cost by filling in each agent's missing report with a resampled one, then estimates the error of that estimate, then the error of the error, and so on. After m rounds the aggregate error is at most 1/Hm mean reports, where Hm is the mth harmonic number. The proof of this bound is the heart of the paper and, unusually for a result about payments, uses complex analysis: a trigonometric representation of the shortfall function together with the Poisson-Jensen inequality for bounded analytic functions in the upper half plane.
