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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.

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File URL: http://repec.imdea.org/pdf/imdea-wp2009-08.pdf
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Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2009-08.

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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
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Web page: http://www.cienciassociales.imdea.org/
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  1. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  2. 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.
  3. Hospido, Laura, 2010. "Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages," IZA Discussion Papers 4712, Institute for the Study of Labor (IZA).
  4. 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).
  5. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  6. Roberto Serrano, 2004. "On Watson’s Non-Forcing Contracts and Renegotiation," Working Papers 2004-03, Brown University, Department of Economics.
  7. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  8. Repullo, Rafael & Saurina, Jesús & Trucharte, Carlos, 2009. "Mitigating the Procyclicality of Basel II," CEPR Discussion Papers 7382, C.E.P.R. Discussion Papers.
  9. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
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  11. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
  12. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  13. 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.
  14. Max Bruche & Javier Suarez, 2009. "The Macroeconomics of Money Market Freezes," Working Papers wp2009_0901, CEMFI.
  15. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
  16. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  17. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
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  19. Enrique Moral-Benito, 2010. "Determinants of economic growth: A Bayesian panel data approach," Working Papers 1031, Banco de España;Working Papers Homepage.
  20. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  21. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-792, May.
  22. 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.
  23. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  24. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
  25. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February.
  26. Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Working Papers 0929, Banco de España;Working Papers Homepage.
  27. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  28. 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.
  29. Dilip Mookherjee & Stefan Reichelstein, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 453-475.
  30. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  31. 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.
  32. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series 1146, The University of Melbourne.
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  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. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
  36. 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.
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  38. 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.
  39. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
  40. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
  41. 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.
  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. repec:cmf:wpaper:wp2008_0801 is not listed on IDEAS
  44. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, and Debt Valuation," Working Papers wp2009_0902, CEMFI.
  45. repec:cmf:wpaper:wp2007_0710 is not listed on IDEAS
  46. 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.
  47. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
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