IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

  • Serrano, Roberto
  • Vohra, Rajiv

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6VBY-508PPXJ-2/2/e62e114199618e182f13fba0908510c6
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 5 (September)
Pages: 775-785

as
in new window

Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:775-785
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. Arellano, Manuel & Hansen, Lars Peter & Sentana, Enrique, 2012. "Underidentification?," Journal of Econometrics, Elsevier, vol. 170(2), pages 256-280.
  3. Enrique Moral-Benito, 2010. "Determinants of economic growth: A Bayesian panel data approach," Banco de Espa�a Working Papers 1031, Banco de Espa�a.
  4. 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.
  5. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers 2006-20, Brown University, Department of Economics.
  6. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  7. Bruche, Max & Suarez, Javier, 2009. "The Macroeconomics of Money Market Freezes," CEPR Discussion Papers 7304, C.E.P.R. Discussion Papers.
  8. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía.
  9. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  10. Roberto Serrano & Rene Saran, 2007. "The Evolution Of Bidding Behavior In Private-Values Auctions And Double Auctions," Working Papers wp2007_0712, CEMFI.
  11. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  12. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  13. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  14. Rafael Repullo & David Martínez-Miera, 2008. "Does Competition Reduce The Risk Of Bank Failure?," Working Papers wp2008_0801, CEMFI.
  15. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  16. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
  17. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  18. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 902, University of Warwick, Department of Economics.
  19. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 453-75, July.
  20. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  21. Rafael Repullo & Jesús Saurina & Carlos Trucharte, 2009. "Mitigating The Procyclicality Of Basel Ii," Working Papers wp2009_0903, CEMFI.
  22. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  23. 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).
  24. Laura Hospido, 2007. "Modelling heterogeneity and dynamics in the volatility of individual wages," Banco de Espa�a Working Papers 0738, Banco de Espa�a.
  25. 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.
  26. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C65-C101, November.
  27. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  28. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  29. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  30. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer, vol. 1(1), pages 41-54, December.
  31. 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.
  32. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  33. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  34. 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.
  35. 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.
  36. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  37. 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.
  38. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  39. 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.
  40. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  41. Roberto Serrano, 2007. "Cooperative Games: Core And Shapley Value," Working Papers wp2007_0709, CEMFI.
  42. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  43. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  44. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  45. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:775-785. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.