Impossibility Results for Truthful Combinatorial Auctions with Submodular Valuations
Impossibility Results for Truthful Combinatorial Auctions with Submodular Valuations
复制标题
具有子模估值的真实组合拍卖的不可能结果
作者：
Shahar Dobzinski;Jan Vondrák
算法机制设计中的一个长期开放的问题是，是否存在合并拍卖的计算有效的真实机制，并且在本文中，我们的绩效保证了接近可能的绩效。动态的机制能够更准确地说，我们表明，具有近似于M1/2-ε近似最佳社会福利的组合式拍卖的每个普遍真实的随机机制使用指数的许多值查询，其中M是项目的数量。 - AppRoximation将暗示NP = RP，忽略了此问题的恒定因素近似算法，并且忽略了计算效率，VCG机制是真实的，并且提供了最佳的社交福利。 - 任何类型的组合拍卖的机制，即使是确定性机制，我们的方法都是基于一种新颖的直接硬度技术，该技术完全跳过了臭名昭著的硬性步骤。机构设计到目前为止。
A long-standing open question in algorithmic mechanism design is whether there exist computationally efficient truthful mechanisms for combinatorial auctions, with performance guarantees close to those possible without considerations of truthfulness. In this article, we answer this question negatively: the requirement of truthfulness can impact dramatically the ability of a mechanism to achieve a good approximation ratio for combinatorial auctions. More precisely, we show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that approximates optimal social welfare within a factor of m1/2−ε must use exponentially many value queries, where m is the number of items. Furthermore, we show that there exists a class of succinctly represented submodular valuation functions, for which the existence of a universally truthful polynomial-time mechanism that provides an m1/2−ε-approximation would imply NP = RP. In contrast, ignoring truthfulness, there exist constant-factor approximation algorithms for this problem, and ignoring computational efficiency, the VCG mechanism is truthful and provides optimal social welfare. These are the first hardness results for truthful polynomial-time mechanisms for any type of combinatorial auctions, even for deterministic mechanisms. Our approach is based on a novel direct hardness technique that completely skips the notoriously hard step of characterizing truthful mechanisms. The characterization step was the main obstacle for proving impossibility results in algorithmic mechanism design so far.