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Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

  • Roberto Serrano

    ()

    (Brown University and IMDEA Social Sciences)

  • Rajiv Vohra

    ()

    (Brown University)

We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima's measurability, there by implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.

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File URL: http://repec.imdea.org/pdf/imdea-wp2009-08.pdf
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Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2009-08.

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Date of creation: 21 Sep 2009
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Publication status: Published in Journal of Mathematical Economics 46(5), September 2010: 775-785
Handle: RePEc:imd:wpaper:wp2009-08
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  13. Roberto Serrano, 2009. "On Watson'S Non-Forcing Contracts And Renegotiation," Working Papers wp2009_0907, CEMFI.
  14. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI.
  15. Max Bruche & Javier Suarez, 2009. "The Macroeconomics Of Money Market Freezes," Working Papers wp2009_0901, CEMFI.
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  19. Chakravorti, Bhaskar, 1992. "Efficiency and Mechanisms with No Regret," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 45-59, February.
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  21. Allan M Feldman & Roberto Serrano, 2007. "Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers 2007-12, Brown University, Department of Economics.
  22. Enrique Sentana & Javier Mencía, 2008. "Distributional Tests In Multivariate Dynamic Models With Normal And Student T Innovations," Working Papers wp2008_0804, CEMFI.
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  24. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  25. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
  26. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
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  34. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 453-75, July.
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  37. Rene Saran & Roberto Serrano, 2007. "The Evolution of Bidding Behavior in Private-Values Auction and Double Auctions," Working Papers 2007-01, Brown University, Department of Economics.
  38. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  39. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  40. Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers wp2008_0807, CEMFI.
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  42. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers wp2007_0711, CEMFI.
  43. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," Discussion Papers in Economics 09/10, Department of Economics, University of Leicester, revised Jan 2010.
  44. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  45. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
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