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Finite supermodular design with interdependent valuations

  • Mathevet, Laurent
  • Taneva, Ina

This paper studies supermodular mechanism design in environments with arbitrary (finite) type spaces and interdependent valuations. In these environments, the designer may have to use Bayesian equilibrium as a solution concept, because ex-post implementation may not be possible. We propose direct (Bayesian) mechanisms that are robust to certain forms of bounded rationality while controlling for equilibrium multiplicity. In quasi-linear environments with informational and allocative externalities, we show that any Bayesian mechanism that implements a social choice function can be converted into a supermodular mechanism that also implements the original decision rule. The proposed supermodular mechanism can be chosen in a way that minimizes the size of the equilibrium set, and we provide two sets of sufficient conditions to this effect. This is followed by conditions for supermodular implementation in unique equilibrium.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 82 (2013)
Issue (Month): C ()
Pages: 327-349

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Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:327-349
DOI: 10.1016/j.geb.2013.07.006
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  9. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
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  15. Ledyard, John O., . "The Scope of the Hypothesis of Bayesian Equilibrium," Working Papers 532, California Institute of Technology, Division of the Humanities and Social Sciences.
  16. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-59, September.
  17. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
  18. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," Levine's Bibliography 666156000000000548, UCLA Department of Economics.
  19. Bergemann, Dirk & Stephen Morris, 2006. "Robust Implementation in Direct Mechanisms," Cowles Foundation Discussion Papers 1561R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  20. Jeffrey C. Ely & Kim-Sau Chung, 2002. "Ex-Post Incentive Compatible Mechanism Design," Discussion Papers 1339, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  22. Jehiel, Philippe & Benny Moldovanu, 1994. "Strategic Non-Participation," Discussion Paper Serie B 287, University of Bonn, Germany.
  23. Mathevet, Laurent A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
  24. 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.
  25. Healy, Paul J., 2006. "Learning dynamics for mechanism design: An experimental comparison of public goods mechanisms," Journal of Economic Theory, Elsevier, vol. 129(1), pages 114-149, July.
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  27. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
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