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Multiple Equilibria as a Difficulty in Understanding Correlated Distributions

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Author Info
Anirban Kar, Indrajit Ray and Robedrto Serrano

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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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Publisher 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
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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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Related research
Keywords: Correlated Equilibrium Distribution; Implementation; Monotonicity;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
  2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January. [Downloadable!] (restricted)
  3. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November. [Downloadable!] (restricted)
    Other versions:
    • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem, revised Nov 2002. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January. [Downloadable!] (restricted)
  6. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer, vol. 30(1), pages 41-60. [Downloadable!] (restricted)
  7. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November. [Downloadable!] (restricted)
  8. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  9. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January. [Downloadable!] (restricted)
  10. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  11. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics. [Downloadable!]
  12. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, vol. 25(2), pages 177-88.
  13. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
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  14. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August. [Downloadable!] (restricted)
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  15. Forges, Francoise, 1990. "Universal Mechanisms," Econometrica, Econometric Society, vol. 58(6), pages 1341-64, November. [Downloadable!] (restricted)
  16. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  17. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July. [Downloadable!] (restricted)
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  18. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
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