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Multiplicity of Mixed Equilibria in Mechanisms: A Unified Approach to Exact and Approximate Implementation

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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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File URL: http://www.cemfi.es/ftp/wp/0908.pdf
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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
Handle: RePEc:cmf:wpaper:wp2009_0908
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  1. 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.
  2. Hospido, Laura, 2010. "Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages," IZA Discussion Papers 4712, Institute for the Study of Labor (IZA).
  3. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," Working Papers wp2009_0905, CEMFI.
  4. Bentolila, Samuel & Dolado, Juan José & Jimeno, Juan F., 2007. "Does Immigration Affect the Phillips Curve? Some Evidence for Spain," Kiel Working Papers 1333, Kiel Institute for the World Economy (IfW).
  5. 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.
  6. 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.
  7. Roberto Serrano, 2009. "On Watson'S Non-Forcing Contracts And Renegotiation," Working Papers wp2009_0907, CEMFI.
  8. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
  9. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers 2006-20, Brown University, Department of Economics.
  10. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  11. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
  12. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  13. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  14. 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.
  15. Stefano Gagliarducci & Tommaso Nannicini & Paolo Naticchioni, 2007. "Electoral Rules And Politicians' Behavior: A Micro Test," Working Papers wp2007_0716, CEMFI.
  16. Roberto Serrano & Allan M. Feldman, 2007. "Arrow’S Impossibility Theorem: Preference Diversity In A Single-Profile World," Working Papers wp2007_0710, CEMFI.
  17. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  18. Rafael Repullo & David Martínez-Miera, 2008. "Does Competition Reduce The Risk Of Bank Failure?," Working Papers wp2008_0801, CEMFI.
  19. Roberto Serrano & Rene Saran, 2007. "The Evolution Of Bidding Behavior In Private-Values Auctions And Double Auctions," Working Papers wp2007_0712, CEMFI.
  20. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
  21. Bruche, Max & Suarez, Javier, 2009. "The Macroeconomics of Money Market Freezes," CEPR Discussion Papers 7304, C.E.P.R. Discussion Papers.
  22. Mendez, Ildefonso, 2008. "Promoting Permanent Employment: Lessons from Spain," MPRA Paper 7933, University Library of Munich, Germany.
  23. Rafael Repullo & Jesús Saurina & Carlos Trucharte, 2009. "Mitigating The Procyclicality Of Basel Ii," Working Papers wp2009_0903, CEMFI.
  24. 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 144-174, August.
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