Econometrica: Jul 2019, Volume 87, Issue 4
Equivalence of Stochastic and Deterministic Mechanisms
Yi‐Chun Chen, Wei He, Jiangtao Li, Yeneng Sun
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.
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Supplement to "Equivalence of Stochastic and Deterministic Mechanisms"
This appendix contains material not found within the manuscript.