Equivalence of Stochastic and Deterministic Mechanisms

Yi-Chun Chen, Wei He, Jiangtao Li, Yeneng Sun

Econometrica · 2019 · Volume 87 · Issue 4

Abstract

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.

Keywords

Deterministic mechanism, stochastic mechanism, mechanism equivalence, mutual purification, reduced-form implementation

Enable JavaScript for citation tools and additional paper interactions.