机构设计中的伯努利工厂和黑盒约简

S. Dughmi, Jason D. Hartline, Robert D. Kleinberg, Rad Niazadeh
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引用次数: 8

摘要

给出了福利最大化问题的贝叶斯激励相容机制设计到贝叶斯算法设计的多项式时间缩减。与先前的结果不同,我们的约简对具有多维和连续类型空间的问题实现了精确的激励相容。在先前的黑盒约简中,阻碍激励兼容的关键技术障碍是,修复违反激励约束的行为需要理解机制产出的分布,这通常是很难计算的。通过抽样来估计输出分布的减少不可避免地会受到抽样误差的影响,这通常会排除精确的激励兼容性。我们通过采用和推广伯努利工厂文献中的计算模型来克服这一障碍。在伯努利工厂问题中,给定一个映射“输入币”到“输出币”偏差的函数,挑战是在只给定输入币的样本访问权限的情况下有效地模拟输出币。这是设计二部匹配激励相容机制的关键要素,它可以使Hartline等[18]的近似激励相容约简完全激励相容。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bernoulli Factories and Black-box Reductions in Mechanism Design
We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces. The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism’s output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility. We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories. In a Bernoulli factory problem, one is given a function mapping the bias of an “input coin” to that of an “output coin,” and the challenge is to efficiently simulate the output coin given only sample access to the input coin. This is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of Hartline et al. [18] exactly incentive compatible.
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