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Ex Post Implementation

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Abstract

We analyze the problem of fully implementing a social choice set in ex post equilibrium. Weidentify 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 monotonicityno veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints. In many economically significant environments, ex post implementation can be achieved in the direct mechanism. We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity (necessary and almost sufficient for complete information implementation). The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. Ex post implementation in the direct mechanism is also possible in this case. We describe an example where the Pareto correspondence fails ex post monotonicity but Maskin monotonicity is satisfied.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1502.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1502.

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Length: 62 pages
Date of creation: Apr 2005
Date of revision:
Publication status: Published in Games and Economic Behavior (2008), 63: 527-566
Handle: RePEc:cwl:cwldpp:1502

Note: CFP 1226.
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Keywords: Ex post equilibrium; Implementation; Single crossing; Interdependent values;

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References

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  1. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  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.
  3. Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation," Economics Working Papers 0056, Institute for Advanced Study, School of Social Science.
  4. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  5. 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 345-61, March.
  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, 05.
  7. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  8. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
  9. Oleksii Birulin, 2003. "Inefficient ex-post equilibria in efficient auctions," Economic Theory, Springer, vol. 22(3), pages 675-683, October.
  10. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation for Research in Economics, Yale University.
  11. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  12. P. Dasgupta & Eric Maskin, 1998. "Efficient Auctions," Harvard Institute of Economic Research Working Papers 1857, Harvard - Institute of Economic Research.
  13. Sushil Bikhchandani, 2004. "The Limits of Ex Post Implementation Revisited," Levine's Bibliography 122247000000000514, UCLA Department of Economics.
  14. Fieseler, Karsten & Kittsteiner, Thomas & Moldovanu, Benny, 2003. "Partnerships, lemons, and efficient trade," Journal of Economic Theory, Elsevier, vol. 113(2), pages 223-234, December.
  15. 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.
  16. Bikhchandani, Sushil, 2006. "Ex post implementation in environments with private goods," Theoretical Economics, Econometric Society, vol. 1(3), pages 369-393, September.
  17. Bengt Holmstrom & Roger B. Myerson, 1981. "Efficient and Durable Decision Rules with Incomplete Information," Discussion Papers 495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Neeman, Z., 1998. "The Relevance of Private Infromation in Mechanism Design," Papers 93, Boston University - Department of Economics.
  19. Dirk Bergemann & Stephen Morris, 2006. "Robust Implementation: The Case of Direct Mechanisms," Levine's Bibliography 122247000000001194, UCLA Department of Economics.
  20. 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.
  21. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  23. 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 668-91, June.
  24. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  25. repec:wop:humbsf:2000-72 is not listed on IDEAS
  26. Manishi Prasad & Peter Wahlqvist & Rich Shikiar & Ya-Chen Tina Shih, 2004. "A," PharmacoEconomics, Springer Healthcare | Adis, vol. 22(4), pages 225-244.
  27. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
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