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Multiple Equilibria as a Difficulty in Understanding Correlated Distributions

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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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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2005-10.

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Date of creation: 2005
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Handle: RePEc:bro:econwp:2005-10

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Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. 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).
  2. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
  3. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
  4. FORGES, Françoise, . "Universal mechanisms," CORE Discussion Papers RP -914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Ehud Lehrer & Sylvain Sorin, 1994. "One-Shot Public Mediated Talk," Discussion Papers 1108, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  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. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  9. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  10. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer, vol. 30(1), pages 41-60.
  11. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  12. 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.
  13. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, 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.
  15. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  16. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  17. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
  18. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, vol. 25(2), pages 177-88.
  19. 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.
  20. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
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