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On the foundations of ex post incentive compatible mechanisms

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  • Takuro Yamashita

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Shuguang Zhu

    (Shanghai University of Finance and Economics)

Abstract

In private-value auction environments, Chung and Ely (2007) establish maxmin and Bayesian foundations for dominant-strategy mechanisms. We first show that similar foundation results for ex post mechanisms hold true even with interdependent values if the interdependence is only cardinal. This includes, for example, the one-dimensional environments of Dasgupta and Maskin (2000) and Bergemann and Morris (2009b). Conversely, if the environment exhibits ordinal interdependence, which is typically the case with multi-dimensional environments (e.g., a player's private information)

Suggested Citation

  • Takuro Yamashita & Shuguang Zhu, 2022. "On the foundations of ex post incentive compatible mechanisms," Post-Print hal-03863573, HAL.
    • Handle: RePEc:hal:journl:hal-03863573
    DOI: 10.1257/mic.20200174
    Note: View the original document on HAL open archive server: https://hal.science/hal-03863573
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    References listed on IDEAS

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    1. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 447-476.
    2. Ilya Segal, 2003. "Optimal Pricing Mechanisms with Unknown Demand," American Economic Review, American Economic Association, vol. 93(3), pages 509-529, June.
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    4. ,, 2006. "Ex post implementation in environments with private goods," Theoretical Economics, Econometric Society, vol. 1(3), pages 369-393, September.
    5. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    6. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    7. Songzi Du, 2018. "Robust Mechanisms Under Common Valuation," Econometrica, Econometric Society, vol. 86(5), pages 1569-1588, September.
    8. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    9. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    10. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    12. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-1115, September.
    13. Takuro Yamashita, 2015. "Implementation in Weakly Undominated Strategies: Optimality of Second-Price Auction and Posted-Price Mechanism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1223-1246.
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    Cited by:

    1. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2022. "Restricted environments and incentive compatibility in interdependent values models," Games and Economic Behavior, Elsevier, vol. 131(C), pages 1-28.
    2. Satoshi Nakada & Shmuel Nitzan & Takashi Ui, 2022. "Robust Voting under Uncertainty," Working Papers on Central Bank Communication 038, University of Tokyo, Graduate School of Economics.
    3. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    4. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    5. Pham, Hien & Yamashita, Takuro, 2021. "Auction Design with Heterogeneous Priors," TSE Working Papers 21-1260, Toulouse School of Economics (TSE), revised Mar 2023.
    6. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    7. Tilman Börgers, 2017. "(No) Foundations of dominant-strategy mechanisms: a comment on Chung and Ely (2007)," Review of Economic Design, Springer;Society for Economic Design, vol. 21(2), pages 73-82, June.

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    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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