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Robust Implementation in Direct Mechanisms

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  • Dirk Bergemann
  • Stephen Morris

Abstract

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages lead to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent-value environment with single-crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too high. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one. Copyright 2009, Wiley-Blackwell.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 814577000000000109.

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Date of creation: 04 Feb 2009
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Handle: RePEc:cla:levarc:814577000000000109

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References

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  2. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," UCLA Economics Working Papers 839, UCLA Department of Economics.
  3. Dirk Bergemann & Stephen Morris, 2007. "Strategic Distinguishability and Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2008.
  4. Stephen Morris & Dirk Bergemann, 2007. "An Ascending Auction for Interdependent Values: Uniqueness and Robustness to Strategic Uncertainty," American Economic Review, American Economic Association, vol. 97(2), pages 125-130, May.
  5. Piketty, Thomas, 1999. "The information-aggregation approach to political institutions," European Economic Review, Elsevier, vol. 43(4-6), pages 791-800, April.
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  10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
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  18. Gresik, Thomas A., 1991. "Ex ante incentive efficient trading mechanisms without the private valuation restriction," Journal of Economic Theory, Elsevier, vol. 55(1), pages 41-63, October.
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  20. Fieseler, Karsten & Kittsteiner, Thomas & Moldovanu, Benny, 1999. "Partnerships, Lemons and Efficient Trade," Sonderforschungsbereich 504 Publications 99-71, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  21. 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.
  22. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
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Citations

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Cited by:
  1. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
  2. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.
  3. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2012. "The Strategic Impact of Higher-Order Beliefs," Levine's Working Paper Archive 786969000000000517, David K. Levine.
  4. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-29, May.
  5. Tomala, Tristan & Renou, Ludovic, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
  6. Carrasco, Vinicius & Salgado, Pablo, 2014. "Coordinated strategic defaults and financial fragility in a costly state verification model," Journal of Financial Intermediation, Elsevier, vol. 23(1), pages 129-139.
  7. 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.
  8. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  9. Meyer-ter-Vehn, Moritz & Morris, Stephen, 2011. "The robustness of robust implementation," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2093-2104, September.
  10. Hernández, Penélope & Muñoz-Herrera, Manuel & Sánchez, Ángel, 2013. "Heterogeneous network games: Conflicting preferences," Games and Economic Behavior, Elsevier, vol. 79(C), pages 56-66.
  11. Diego Moreno & María Moscoso, 2013. "Strategy-proof allocation mechanisms for economies with public goods," Economic Theory, Springer, vol. 52(1), pages 315-336, January.
  12. Felix Bierbrauer & Martin Hellwig, 2011. "Mechanism Design and Voting for Public-Good Provision," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2011_31, Max Planck Institute for Research on Collective Goods.
  13. Beard, Rodney & Mallawaarachchi, Thilak, 2011. "Are international environmental agreements stable ex-post?," MPRA Paper 34303, University Library of Munich, Germany.
  14. Di Tillio, Alfredo, 2011. "A robustness result for rationalizable implementation," Games and Economic Behavior, Elsevier, vol. 72(1), pages 301-305, May.

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