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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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  4. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  5. Javier Mencía & Enrique Sentana, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Banco de Espa�a Working Papers 0909, Banco de Espa�a.
  6. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  7. Roberto Serrano, 2004. "On Watson’s Non-Forcing Contracts and Renegotiation," Working Papers 2004-03, Brown University, Department of Economics.
  8. Hospido, Laura, 2010. "Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages," IZA Discussion Papers 4712, Institute for the Study of Labor (IZA).
  9. Repullo, Rafael & Saurina, Jesús & Trucharte, Carlos, 2009. "Mitigating the Procyclicality of Basel II," CEPR Discussion Papers 7382, C.E.P.R. Discussion Papers.
  10. 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.
  11. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  12. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  13. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 902, University of Warwick, Department of Economics.
  14. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  15. 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.
  16. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
  17. Enrique Moral-Benito, 2012. "Determinants of Economic Growth: A Bayesian Panel Data Approach," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 566-579, May.
  18. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," Working Papers wp2009_0905, CEMFI.
  19. Stefano Gagliarducci & Tommaso Nannicini & Paolo Naticchioni, 2011. "Electoral Rules and Politicians' Behavior: A Micro Test," American Economic Journal: Economic Policy, American Economic Association, vol. 3(3), pages 144-74, August.
  20. Roberto Serrano, 2007. "Cooperative Games: Core And Shapley Value," Working Papers wp2007_0709, CEMFI.
  21. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  22. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  23. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  24. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  25. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
  26. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  27. 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.
  28. 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.
  29. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  30. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  31. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  32. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer, vol. 1(1), pages 41-54, December.
  33. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  34. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  35. Bruche, Max & Suarez, Javier, 2009. "The Macroeconomics of Money Market Freezes," CEPR Discussion Papers 7304, C.E.P.R. Discussion Papers.
  36. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  37. 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.
  38. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  39. Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Banco de Espa�a Working Papers 0929, Banco de Espa�a.
  40. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  41. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  42. 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.
  43. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 453-75, July.
  44. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  45. 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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