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Ex-post implementation and preference aggregation via potentials

Author

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  • Philippe Jehiel

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London])

  • Moritz Meyer-Ter-Vehn

    (UCLA - University of California [Los Angeles] - UC - University of California)

  • Benny Moldovanu

    (Universität Bonn = University of Bonn)

Abstract

We introduce several notions of potentials for mechanism design problems with interdependent values, and relate them to implementation in ex-post equilibrium. Whereas ex-post implementation is closely linked to the ordinal concept of best-alternative potentials, the celebrated Vickrey-Clarke-Groves mechanism corresponds to the stronger notion of a cardinal potential: agents agree not only on the best alternative, but also on the quantitative differences between all alternatives. We characterize all valuations that allow for cardinal potentials, and use this characterization for: (1) Identifying valuations for which ex-post implementation is possible; (2) Identifying classes of valuations for which all ex-post implementable choice rules correspond to cardinal potentials. The latter allows us to extend to interdependent valuations a result for dominant strategy implementation in private values settings, due to Roberts (The Characterization of Implementable Choice Rules, North-Holland, Amsterdam, 1979).

Suggested Citation

  • Philippe Jehiel & Moritz Meyer-Ter-Vehn & Benny Moldovanu, 2008. "Ex-post implementation and preference aggregation via potentials," Post-Print halshs-00754256, HAL.
    • Handle: RePEc:hal:journl:halshs-00754256
    DOI: 10.1007/s00199-007-0300-1
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    Cited by:

    1. Mishra, Debasis & Sen, Arunava, 2012. "Robertsʼ Theorem with neutrality: A social welfare ordering approach," Games and Economic Behavior, Elsevier, vol. 75(1), pages 283-298.
    2. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    3. Mishra, Debasis & Nath, Swaprava & Roy, Souvik, 2018. "Separability and decomposition in mechanism design with transfers," Games and Economic Behavior, Elsevier, vol. 109(C), pages 240-261.
    4. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    5. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    6. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2012. "Locally robust implementation and its limits," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2439-2452.
    7. Jacob K. Goeree & Alexey Kushnir, 2011. "On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems," ECON - Working Papers 021, Department of Economics - University of Zurich.
    8. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
    9. Alfred Galichon, 2021. "Fritz John’s equation in mechanism design," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 1-5, April.
    10. Dobzinski, Shahar & Nisan, Noam, 2015. "Multi-unit auctions: Beyond Roberts," Journal of Economic Theory, Elsevier, vol. 156(C), pages 14-44.
    11. Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Discussion Papers 12-06, Indian Statistical Institute, Delhi.
    12. Ron Lavi & Ahuva Mu’alem & Noam Nisan, 2009. "Two simplified proofs for Roberts’ theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 407-423, March.
    13. Dizdar, Deniz & Moldovanu, Benny, 2016. "On the importance of uniform sharing rules for efficient matching," Journal of Economic Theory, Elsevier, vol. 165(C), pages 106-123.
    14. Debasis Mishra & Abdul Quadir, 2014. "Non-bossy single object auctions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 93-110, April.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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