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Multiple Equilibria as a Difficulty in Understanding Correlated Distributions

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  • Anirban Kar, Indrajit Ray and Robedrto Serrano

Abstract

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: ftp://ftp.bham.ac.uk/pub/RePEc/pdf/karrayserrano.pdf
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Bibliographic Info

Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 05-18.

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Length: 12 pages
Date of creation: Nov 2005
Date of revision:
Handle: RePEc:bir:birmec:05-18

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Postal: Edgbaston, Birmingham, B15 2TT
Web page: http://www.economics.bham.ac.uk
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Keywords: Correlated Equilibrium Distribution; Implementation; Monotonicity;

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  1. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  2. Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Nov 2002.
  3. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  4. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
  5. Forges, F., 1987. "Universal mechanisms," CORE Discussion Papers 1987004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
  7. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  8. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  9. Dino Gerardi, 2002. "Unmediated Communication in Games with Complete and Incomplete Information," Cowles Foundation Discussion Papers 1371, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
  12. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  13. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
  14. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  16. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  17. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, vol. 25(2), pages 177-88.
  18. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August.
  19. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer, vol. 30(1), pages 41-60.
  20. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
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