IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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

Listed author(s):
  • Roberto Serrano

    ()

    (Brown University and IMDEA Social Sciences)

  • Rajiv Vohra

    ()

    (Brown University)

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, there by 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://repec.imdea.org/pdf/imdea-wp2009-08.pdf
Download Restriction: no

Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2009-08.

as
in new window

Length:
Date of creation: 21 Sep 2009
Publication status: Published in Journal of Mathematical Economics 46(5), September 2010: 775-785
Handle: RePEc:imd:wpaper:wp2009-08
Contact details of provider: Postal:
Veláquez 76, 28001 Madrid

Phone: +34917816570
Fax: +34916766052
Web page: http://www.cienciassociales.imdea.org/
Email:


More information through EDIRC

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. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
  2. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
  3. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
  4. Bentolila, Samuel & Dolado, Juan J. & Jimeno, Juan F., 2008. "Does immigration affect the Phillips curve? Some evidence for Spain," European Economic Review, Elsevier, vol. 52(8), pages 1398-1423, November.
  5. 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.
  6. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  7. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
  8. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
  9. 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.
  10. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  11. 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.
  12. 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.
  13. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 193-208.
  14. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
  15. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  16. L. Hospido, 2012. "Modelling heterogeneity and dynamics in the volatility of individual wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 386-414, 04.
  17. 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.
  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 144-174, August.
  19. Dilip Mookherjee & Stefan Reichelstein, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 453-475.
  20. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  21. 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.
  22. Bruche, Max & Suarez, Javier, 2009. "The Macroeconomics of Money Market Freezes," CEPR Discussion Papers 7304, C.E.P.R. Discussion Papers.
  23. 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.
  24. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
  25. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  26. 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.
  27. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, and Debt Valuation," Working Papers wp2009_0902, CEMFI.
  28. Ildefonso Mendez, 2013. "Promoting permanent employment: lessons from Spain," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 175-199, June.
  29. 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.
  30. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  31. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
  32. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  33. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  34. 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.
  35. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  36. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
  37. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
  38. 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.
  39. 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.
  40. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
  41. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-792, May.
  42. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, 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:imd:wpaper:wp2009-08. 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: (IMDEA RePEc Maintainer)

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.