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Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach ot Exact and Approximate Implementation

We characterize full implementation of social choice sets in mixedstrategy 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 Brown University, Department of Economics in its series Working Papers with number 2009-11.

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Date of creation: 2009
Date of revision:
Handle: RePEc:bro:econwp:2009-11
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  2. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C65-C101, November.
  3. Roberto Serrano & Antonio Cabrales, 2007. "Implemetation In Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
  4. 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.
  5. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  6. Javier Mencía & Enrique Sentana, 2012. "Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 133-152, February.
  7. Hospido, Laura, 2010. "Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages," IZA Discussion Papers 4712, Institute for the Study of Labor (IZA).
  8. 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.
  9. Samuel Bentolila & Juan Jose Dolado & Juan F. Jimeno, 2007. "Does Immigration Affect the Phillips Curve? Some Evidence for Spain," CESifo Working Paper Series 2166, CESifo Group Munich.
  10. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
  11. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
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  13. 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.
  14. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  15. Rafael Repullo & Jes�s Saurina & Carlos Trucharte, 2010. "Mitigating the pro-cyclicality of Basel II," Economic Policy, CEPR;CES;MSH, vol. 25, pages 659-702, October.
  16. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  17. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  18. 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.
  19. Roberto Serrano, 2004. "On Watson’s Non-Forcing Contracts and Renegotiation," Working Papers 2004-03, Brown University, Department of Economics.
  20. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," CeMMAP working papers CWP24/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  21. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers wp2007_0711, CEMFI.
  22. repec:cwl:cwldpp:1609rr is not listed on IDEAS
  23. Enrique Moral-Benito, 2007. "Determinants Of Economic Growth: A Bayesian Panel Data Approach," Working Papers wp2007_0719, CEMFI.
  24. Repullo, Rafael & Suarez, Javier, 2008. "The Procyclical Effects of Basel II," CEPR Discussion Papers 6862, C.E.P.R. Discussion Papers.
  25. 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.
  26. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
  27. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  28. 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.
  29. 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.
  30. Ildefonso Mendez, 2013. "Promoting permanent employment: lessons from Spain," SERIEs, Spanish Economic Association, vol. 4(2), pages 175-199, June.
  31. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  32. Max Bruche & Javier Suarez, 2009. "The Macroeconomics Of Money Market Freezes," Working Papers wp2009_0901, CEMFI.
  33. 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.
  34. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 193-208.
  35. Roberto Serrano & Allan M. Feldman, 2007. "Arrow’S Impossibility Theorem: Preference Diversity In A Single-Profile World," Working Papers wp2007_0710, CEMFI.
  36. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  37. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer, vol. 1(1), pages 41-54, December.
  38. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  39. Dilip Mookherjee & Stefan Reichelstein, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 453-475.
  40. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  41. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  42. 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.
  43. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  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. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  46. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  47. 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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