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Equivalence of Stochastic and Deterministic Mechanisms

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  • Yi‐Chun Chen
  • Wei He
  • Jiangtao Li
  • Yeneng Sun

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.

Suggested Citation

  • Yi‐Chun Chen & Wei He & Jiangtao Li & Yeneng Sun, 2019. "Equivalence of Stochastic and Deterministic Mechanisms," Econometrica, Econometric Society, vol. 87(4), pages 1367-1390, July.
    • Handle: RePEc:wly:emetrp:v:87:y:2019:i:4:p:1367-1390
    DOI: 10.3982/ECTA14698
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    Cited by:

    1. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. Sano, Ryuji, 2021. "Dynamic slot allocations with different patience levels," Games and Economic Behavior, Elsevier, vol. 130(C), pages 465-473.
    3. Nicolas, Floyid & Kamai, Tamir & Ben-Gal, Alon & Ochoa-Brito, Jose & Daccache, Andre & Ogunmokun, Felix & Kisekka, Isaya, 2023. "Assessing salinity impacts on crop yield and economic returns in the Central Valley," Agricultural Water Management, Elsevier, vol. 287(C).
    4. Axel Niemeyer & Justus Preusser, 2023. "Simple Allocation with Correlated Types," CRC TR 224 Discussion Paper Series crctr224_2023_486, University of Bonn and University of Mannheim, Germany.
    5. Boaz Zik, 2023. "Efficient sequential screening with informational externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 567-590, February.
    6. Pycia, Marek & Woodward, Kyle, 2021. "Auctions of Homogeneous Goods: A Case for Pay-as-Bid," CEPR Discussion Papers 15656, C.E.P.R. Discussion Papers.

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