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Ex Post Implementation

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

Author

Listed:
  • 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
    as

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    References listed on IDEAS

    as
    1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
    2. Arya, Anil & Glover, Jonathan & Rajan, Uday, 2000. "Implementation in Principal-Agent Models of Adverse Selection," Journal of Economic Theory, Elsevier, vol. 93(1), pages 87-109, July.
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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.
    8. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
    9. Motty Perry & Philip J. Reny, 2002. "An Efficient Auction," Econometrica, Econometric Society, vol. 70(3), pages 1199-1212, May.
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    11. 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..
    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.
    13. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    14. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(2), pages 341-388.
    15. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    16. Partha Dasgupta & Peter Hammond & Eric Maskin, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 185-216.
    17. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    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.
    21. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    22. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    23. Oleksii Birulin, 2003. "Inefficient ex-post equilibria in efficient auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 675-683, October.
    24. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    25. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    26. Sushil Bikhchandani, 2004. "The Limits of Ex Post Implementation Revisited," Levine's Bibliography 122247000000000514, UCLA Department of Economics.
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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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