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Ex Post Implementation

In: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs

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  • Dirk Bergemann
  • Stephen Morris

Abstract

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and — in economic environments — sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2012. "Ex Post Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 3, pages 97-152, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814374590_0003
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    1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
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    4. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
    5. Dirk Bergemann & Stephen Morris, 2006. "Robust Implementation: The Case of Direct Mechanisms"," Cowles Foundation Discussion Papers 1561R, Cowles Foundation for Research in Economics, Yale University, revised May 2007.
    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. , & , & ,, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
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    12. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-691, June.
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    18. Yokoo, Makoto & Sakurai, Yuko & Matsubara, Shigeo, 2004. "The effect of false-name bids in combinatorial auctions: new fraud in internet auctions," Games and Economic Behavior, Elsevier, vol. 46(1), pages 174-188, January.
    19. ,, 2006. "Ex post implementation in environments with private goods," Theoretical Economics, Econometric Society, vol. 1(3), pages 369-393, September.
    20. Fieseler, Karsten & Kittsteiner, Thomas & Moldovanu, Benny, 2003. "Partnerships, lemons, and efficient trade," Journal of Economic Theory, Elsevier, vol. 113(2), pages 223-234, December.
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    22. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
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    More about this item

    Keywords

    Mechanism Design; Game Theory; Auction Theory; Implementation; Private Information; First and Higher-Order Belief; BayesNash Equilibrium; Ex Post Equilibrium; Rationalizability; Vickrey-Clarke-Groves Mechanisms; Private Value; Interdependent Value; Common Value; Belief-Free Mechanisms;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D0 - Microeconomics - - General

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