公共项目、布尔函数和边界定理的边界

Parikshit Gopalan, N. Nisan, T. Roughgarden
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引用次数: 27

摘要

Border定理给出了贝叶斯单项目环境下可行的临时分配规则的直观线性表征,在经济和算法机制设计中具有广泛的应用。所有已知的博德定理的推广,要么将注意力限制在相对简单的情况下,要么求助于近似。本文确定了一个复杂性理论障碍,它表明,假设标准的复杂性类分离,边界定理不能显著地扩展到最先进的水平。我们还发现,当应用于公共项目设置时,迈尔森的最优拍卖理论与布尔函数分析中的一些基本结果之间存在惊人的紧密联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Public Projects, Boolean Functions, and the Borders of Border's Theorem
Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border's theorem either restrict attention to relatively simple settings, or resort to approximation. This paper identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state-of-the-art. We also identify a surprisingly tight connection between Myerson's optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions.
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