arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1305.4002cs.GTcs.DS
收藏

理解激励:机制设计成为算法设计

Understanding Incentives: Mechanism Design becomes Algorithm Design

Yang Cai, Constantinos Daskalakis, S. Matthew Weinberg

摘要:

我们提供了一个计算效率的黑箱减少机制设计算法设计在非常一般的设置。具体来说,我们给出了一个近似保持减少如实最大化\emph{any}目标下\emph{arbitrary}可行性约束与\emph{arbitrary}投标人类型(不一定如实)最大化相同的目标加虚拟福利(在相同的可行性约束)。我们的减少是基于一个全新的方法:我们间接地描述一个机制的行为,只在预期价值,它授予投标人的某些行为,从来没有直接访问的分配规则。将我们的新方法应用于收入,我们展示了我们的减少持有\emph{both ways}的设置。也就是说,我们还提供了一个近似敏感的减少(非真实)最大化虚拟福利(真实)最大化收入,因此这两个问题是计算等价的。有了这个等价的手,我们表明,这两个问题是NP-难近似在任何多项式因子,即使是一个单一的单调子模投标人。我们进一步证明了我们的减少的适用性,通过提供一个真实的机制,最大限度地提高分数最大最小公平。这是第一个优化非线性目标的真实机制的实例。

英文摘要:

We provide a computationally efficient black-box reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximation-preserving reduction from truthfully maximizing \emph{any} objective under \emph{arbitrary} feasibility constraints with \emph{arbitrary} bidder types to (not necessarily truthfully) maximizing the same objective plus virtual welfare (under the same feasibility constraints). Our reduction is based on a fundamentally new approach: we describe a mechanism's behavior indirectly only in terms of the expected value it awards bidders for certain behavior, and never directly access the allocation rule at all. Applying our new approach to revenue, we exhibit settings where our reduction holds \emph{both ways}. That is, we also provide an approximation-sensitive reduction from (non-truthfully) maximizing virtual welfare to (truthfully) maximizing revenue, and therefore the two problems are computationally equivalent. With this equivalence in hand, we show that both problems are NP-hard to approximate within any polynomial factor, even for a single monotone submodular bidder. We further demonstrate the applicability of our reduction by providing a truthful mechanism maximizing fractional max-min fairness. This is the first instance of a truthful mechanism that optimizes a non-linear objective.

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。

↑