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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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  8. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  9. Roberto Serrano & Antonio Cabrales, 2007. "Implemetation In Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
  10. Laura Hospido, 2007. "Modelling heterogeneity and dynamics in the volatility of individual wages," Working Papers 0738, Banco de España;Working Papers Homepage.
  11. Bentolila, Samuel & Dolado, Juan J. & Jimeno, Juan F, 2007. "Does Immigration Affect the Phillips Curve? Some Evidence for Spain," CEPR Discussion Papers 6604, C.E.P.R. Discussion Papers.
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  13. Stefano Gagliarducci & Tommaso Nannicini & Paolo Naticchioni, 2007. "Electoral Rules And Politicians' Behavior: A Micro Test," Working Papers wp2007_0716, CEMFI.
  14. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
  15. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
  16. Roberto Serrano & Allan M. Feldman, 2007. "Arrow’S Impossibility Theorem: Preference Diversity In A Single-Profile World," Working Papers wp2007_0710, CEMFI.
  17. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  18. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  19. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  20. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  21. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
  22. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI.
  23. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  24. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  25. Ildefonso Mendez, 2013. "Promoting permanent employment: lessons from Spain," SERIEs- Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 175-199, June.
  26. Roberto Serrano, 2009. "On Watson'S Non-Forcing Contracts And Renegotiation," Working Papers wp2009_0907, CEMFI.
  27. Rene Saran & Roberto Serrano, 2007. "The evolution of bidding behavior in private-values auctions and double auctions," Working Papers 2007-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  28. Arellano, Manuel & Hansen, Lars Peter & Sentana, Enrique, 2012. "Underidentification?," Journal of Econometrics, Elsevier, vol. 170(2), pages 256-280.
  29. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  30. Enrique Moral-Benito, 2007. "Determinants Of Economic Growth: A Bayesian Panel Data Approach," Working Papers wp2007_0719, CEMFI.
  31. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  32. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 41-54, December.
  33. Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI.
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  39. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  40. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  41. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  42. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  43. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  44. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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  46. 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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