Equivalence of Stochastic and Deterministic Mechanisms

• 成果类型: Article
• 署名作者: Chen, Yi-Chun; He, Wei; Li, Jiangtao; Sun, Yeneng
• 署名单位: National University of Singapore; Chinese University of Hong Kong; Singapore Management University; National University of Singapore
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA14698
• 发表日期: 2019
• 页码: 1367-1390
• 关键词: Revelation principle; DESIGN; implementation; purification; INFORMATION; strategies; revenue

摘要

We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.