关于测试单参数分配机制激励相容性的研究
On testing the incentive compatibility of single-parameter allocation mechanisms
浏览论文内容
中文总结 AI 辅助
本文首次将性质检验应用于博弈论，提出测试单参数分配机制激励相容性的算法，给出Õ(n/ε)查询上界与匹配下界，并扩展至定价函数。
中文摘要 AI 辅助
本文是博弈论与性质检验交叉领域的首项工作，给出了高效测试分配机制是否激励相容（IC）的算法与下界。我们提出区分一个机制是否与IC机制ε-远（即观察到大量单调性“违规”）的问题。概念上，受布尔函数单调性检验文献的启发，我们为离散单参数分配规则构建了一个检验器。技术上，本文首次考虑超网格上向量值函数的单调性检验。我们给出了一个Õ(n/ε)查询的算法，用于测试一个表示n个玩家分配机制的函数是坐标单调的还是与其ε-远。我们还证明了匹配的下界：在布尔超立方体或超网格上，坐标单调的向量值函数类需要Ω̃(n/ε)次查询来测试其是否与单调性ε-远，即使检验器是双侧的且允许自适应查询，该下界也成立。最后，我们将上界扩展到分配机制的定价函数，并给出了相同查询复杂度的检验器。这需要克服一个技术挑战：在函数空间中，通往最近IC机制的路径可能涉及价格和分配规则的相互依赖的变化。
英文摘要
This paper is the first work at the intersection of game theory and property testing, giving algorithms and lower bounds for efficiently testing whether an allocation mechanism is incentive compatible (IC). We propose distinguishing whether a mechanism is $ε$-far from being IC, i.e., when it observes many monotonicity "violations." Conceptually, inspired by the literature on Boolean function monotonicity testing, we construct a tester for discrete single-parameter allocation rules. Technically, our work is the first to consider monotonicity testing of vector-valued functions on the hypergrid. We give a $\tilde{O}(n/ε)$-query algorithm to test whether a function (representing n-player allocation mechanisms) is coordinate-wise monotone versus $ε$-far from it. We also show a matching lower bound: the class of coordinate-wise monotone vector-valued functions on a Boolean hypercube or hypergrid requires $\tildeΩ(n/ε)$ queries to test whether it is $ε$-far from monotonicity, and this holds even if the tester is two-sided and allowed to make adaptive queries. Finally, we extend our upper bound to and give a tester of the same query complexity for pricing functions of allocation mechanisms. This requires overcoming the technical challenge that the path in function space to the closest IC mechanism may involve interdependent changes to both the price and the allocation rule.
发表机构
- Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
