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Multiplicity Of Mixed Equilibria In Mechanisms: A Unified Approach To Exact And Approximate Implementation

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, thereby 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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Paper provided by CEMFI in its series Working Papers with number wp2009_0908.

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Date of creation: Sep 2009
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Handle: RePEc:cmf:wpaper:wp2009_0908
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  1. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  2. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  3. Roberto Serrano & Antonio Cabrales, 2007. "Implemetation In Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
  4. 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.
  5. 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.
  6. Mendez, Ildefonso, 2008. "Promoting Permanent Employment: Lessons from Spain," MPRA Paper 7933, University Library of Munich, Germany.
  7. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  8. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  9. Martinez-Miera, David & Repullo, Rafael, 2008. "Does Competition Reduce the Risk of Bank Failure?," CEPR Discussion Papers 6669, C.E.P.R. Discussion Papers.
  10. Samuel Bentolila & Juan J. Dolado & Juan F. Jimeno, 2008. "Does immigration affect the Phillips curve? Some evidence for Spain," Working Papers 0814, Banco de España;Working Papers Homepage.
  11. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
  12. 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.
  13. 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.
  14. Arellano, Manuel & Hansen, Lars Peter & Sentana, Enrique, 2012. "Underidentification?," Journal of Econometrics, Elsevier, vol. 170(2), pages 256-280.
  15. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  16. Robert J. Aumann & Roberto Serrano, 2007. "An economic index of riskiness," Working Papers 2007-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  17. Hospido, Laura, 2010. "Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages," IZA Discussion Papers 4712, Institute for the Study of Labor (IZA).
  18. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  19. 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.
  20. Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers wp2008_0807, CEMFI.
  21. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  22. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  23. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI.
  24. Enrique Moral-Benito, 2007. "Determinants Of Economic Growth: A Bayesian Panel Data Approach," Working Papers wp2007_0719, CEMFI.
  25. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  26. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  27. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  28. Roberto Serrano, 2004. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Working Papers 0041, Institute for Advanced Study, School of Social Science.
  29. Rafael Repullo & Jesús Saurina & Carlos Trucharte, 2010. "Mitigating the pro-cyclicality of Basel II," Economic Policy, CEPR;CES;MSH, vol. 25, pages 659-702, October.
  30. Gagliarducci, Stefano & Nannicini, Tommaso & Naticchioni, Paolo, 2008. "Electoral Rules and Politicians’ Behavior: A Micro Test," IZA Discussion Papers 3348, Institute for the Study of Labor (IZA).
  31. Dilip Mookherjee & Stefan Reichelstein, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 453-475.
  32. Roberto Serrano, 2007. "Cooperative Games: Core And Shapley Value," Working Papers wp2007_0709, CEMFI.
  33. 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.
  34. Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Working Papers 0929, Banco de España;Working Papers Homepage.
  35. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  36. Max Bruche & Javier Suarez, 2009. "The Macroeconomics Of Money Market Freezes," Working Papers wp2009_0901, CEMFI.
  37. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  38. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
  39. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
  40. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  41. 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.
  42. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 193-208.
  43. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  44. 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.
  45. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  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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