Advanced Search
MyIDEAS: Login to save this paper or follow this series

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

Contents:

Author Info

Abstract

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.

Download Info

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.brown.edu/Departments/Economics/Papers/2009/2009-11_paper.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2009-11.

as in new window
Length:
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

Related research

Keywords: Exact implementation; approximate implementation; incomplete information; incentive compatibility; monotonicity;

Other versions of this item:

Find related papers by JEL classification:

References

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. Manuel Arellano & Lars P. Hansen & Enrique Sentana, 2000. "Underidentification?," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1824, Econometric Society.
  2. 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.
  3. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1609RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  4. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series, The Rimini Centre for Economic Analysis 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  5. Enrique Sentana, 2008. "The Econometrics Of Mean-Variance Efficiency Tests: A Survey," Working Papers, CEMFI wp2008_0807, CEMFI.
  6. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series, The University of Melbourne 1146, The University of Melbourne.
  7. Stefano Gagliarducci & Tommaso Nannicini & Paolo Naticchioni, 2007. "Electoral Rules And Politicians' Behavior: A Micro Test," Working Papers, CEMFI wp2007_0716, CEMFI.
  8. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía.
  9. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers, CEMFI wp2009_0902, CEMFI.
  10. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(1), pages 51-67, September.
  11. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
  12. Roberto Serrano, 2007. "Cooperative Games: Core And Shapley Value," Working Papers, CEMFI wp2007_0709, CEMFI.
  13. Bruche, Max & Suarez, Javier, 2009. "The Macroeconomics of Money Market Freezes," CEPR Discussion Papers, C.E.P.R. Discussion Papers 7304, C.E.P.R. Discussion Papers.
  14. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 997-1021, July.
  15. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  17. Repullo, Rafael & Saurina, Jesús & Trucharte, Carlos, 2009. "Mitigating the Procyclicality of Basel II," CEPR Discussion Papers, C.E.P.R. Discussion Papers 7382, C.E.P.R. Discussion Papers.
  18. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers, Brown University, Department of Economics 2007-6, Brown University, Department of Economics.
  19. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, Econometric Society, vol. 60(6), pages 1439-42, November.
  20. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers, Brown University, Department of Economics 2006-20, Brown University, Department of Economics.
  21. Enrique Moral-Benito, 2010. "Determinants of economic growth: A Bayesian panel data approach," Banco de Espa�a Working Papers, Banco de Espa�a 1031, Banco de Espa�a.
  22. Rene Saran & Roberto Serrano, 2007. "The evolution of bidding behavior in private-values auctions and double auctions," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2007-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  23. Roberto Serrano, 2004. "On Watson’s Non-Forcing Contracts and Renegotiation," Working Papers, Brown University, Department of Economics 2004-03, Brown University, Department of Economics.
  24. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, Elsevier, 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.
  25. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 128-144, June.
  26. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(1), pages 14-33, June.
  27. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 785-92, May.
  28. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers, CEMFI wp2008_0809, CEMFI.
  29. Enrique Sentana & Javier Mencía, 2008. "Distributional Tests In Multivariate Dynamic Models With Normal And Student T Innovations," Working Papers, CEMFI wp2008_0804, CEMFI.
  30. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers, CEMFI wp2008_0806, CEMFI.
  31. Allan M Feldman & Roberto Serrano, 2007. "Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers, Brown University, Department of Economics 2007-12, Brown University, Department of Economics.
  32. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer, Springer, vol. 1(1), pages 41-54, December.
  33. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, Elsevier, vol. 153(2), pages 105-121, December.
  34. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  35. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 993-1008, September.
  36. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  37. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers, CEMFI wp2007_0711, CEMFI.
  38. L. Hospido, 2012. "Modelling heterogeneity and dynamics in the volatility of individual wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 27(3), pages 386-414, 04.
  39. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  40. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers, Brown University, Department of Economics 2002-11, Brown University, Department of Economics.
  41. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 45-59, February.
  42. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, Econometric Society, vol. 57(1), pages 115-34, January.
  43. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1175-1200, September.
  44. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(3), pages 453-75, July.
  45. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 107-121, February.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series, The University of Melbourne 1146, The University of Melbourne.
  2. Tomala, Tristan & Renou, Ludovic, 2010. "Mechanism design and communication networks," Les Cahiers de Recherche, HEC Paris 926, HEC Paris.
  3. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1697R, Cowles Foundation for Research in Economics, Yale University.
  4. Ashraf-Ball, Hezlin & Oswald, Andrew J. & Oswald, James I., 2009. "Hydrogen Transport and the Spatial Requirements of Renewable Energy," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 903, University of Warwick, Department of Economics.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:bro:econwp:2009-11. 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: (Brown Economics Webmaster).

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.