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Multiple equilibria as a difficulty in understanding correlated distributions

  • Anirban Kar

    ()

    (University of Warwick)

  • Indrajit Ray

    ()

    (University of Birmingham)

  • Roberto Serrano

    ()

    (Brown University and IMDEA Social Sciences)

We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium.

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File URL: http://repec.imdea.org/pdf/imdea-wp2007-03.pdf
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Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2007-03.

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Date of creation: 28 Feb 2007
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Publication status: Published in Games and Economic Behavior 69(1), May 2010: 189-193
Handle: RePEc:imd:wpaper:wp2007-03
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  1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  2. Ben-Porath, Elchanan, 1998. "Correlation without Mediation: Expanding the Set of Equilibrium Outcomes by "Cheap" Pre-play Procedures," Journal of Economic Theory, Elsevier, vol. 80(1), pages 108-122, May.
  3. FORGES, Françoise, . "Universal mechanisms," CORE Discussion Papers RP -914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  5. Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
  6. GOSSNER, Olivier, 1997. "Secure protocols or how communication generates correlation," CORE Discussion Papers 1997092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
  8. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, vol. 25(2), pages 177-88.
  9. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  10. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  11. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  13. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  14. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August.
  15. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
  16. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer, vol. 30(1), pages 41-60.
  17. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  18. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  19. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
  20. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
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