Equivalence of Stochastic and Deterministic Mechanisms
研究在一般社会选择环境中，任何贝叶斯激励相容的随机机制都存在一个等价的确定性机制，保持相同的临时分配概率、临时期望效用和事前期望社会剩余，适用于多种效用函数和估值情形。
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.