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Correlated Equilibria, Good and Bad: An Experimental Study

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  • John Duffy
  • Nick Feltovich

Abstract

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of the Nash equilibrium concept. Specifically, we seek to understand the conditions under which subjects will condition their behavior on private, third-party recommendations drawn from known distributions in playing the game of Chicken. In a `good-recommendations` treatment, the distribution is such that following recommendations comprises a correlated equilibrium with payoffs better than any symmetric payoff in the convex hull of Nash equilibrium payoff vectors. In a `bad-recommendations` treatment, the distribution is such that following recommendations comprises a correlated equilibrium with payoffs worse than any Nash equilibrium payoff vector. In a `Nash-recommendations` treatment, the distribution is a convex combination of Nash equilibrium outcomes (which is also a correlated equilibrium), and in a fourth `very-good-recommendations` treatment, the distribution yields high payoffs, but following recommendations does not comprise a correlated equilibrium. We compare behavior in all of these treatments to the case where subjects do not receive recommendations. We find that when recommendations are not given to subjects, behavior is very close to mixed-strategy Nash equilibrium play. When recommendations are given, behavior does differ from mixed-strategy Nash equilibrium, with the nature of the differences varying according to the treatment. Our main finding is that subjects will follow third-party recommendations only if those recommendations derive from a correlated equilibrium, and further, if that correlated equilibrium is payoff-enhancing relative to the available Nash equilibria.

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Bibliographic Info

Paper provided by University of Pittsburgh, Department of Economics in its series Working Papers with number 358.

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Date of creation: Jul 2008
Date of revision: Oct 2008
Handle: RePEc:pit:wpaper:358

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  1. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  2. Van Huyck, John B. & Gillette, Ann B. & Battalio, Raymond C., 1992. "Credible assignments in coordination games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 606-626, October.
  3. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer, vol. 10(2), pages 171-178, June.
  4. Seely, Beth & Van Huyck, John & Battalio, Raymond, 2005. "Credible assignments can improve efficiency in laboratory public goods games," Journal of Public Economics, Elsevier, vol. 89(8), pages 1437-1455, August.
  5. Moreno, Diego & Wooders, John, 1996. "Coalition-Proof Equilibrium," Games and Economic Behavior, Elsevier, vol. 17(1), pages 80-112, November.
  6. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
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Cited by:
  1. Dietmar Fehr & Frank Heinemann & Aniol Llorente-Saguer, 2011. "The Power of Sunspots: An Experimental Analysis," SFB 649 Discussion Papers SFB649DP2011-070, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Oprea, Ryan & Henwood, Keith & Friedman, Daniel, 2011. "Separating the Hawks from the Doves: Evidence from continuous time laboratory games," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2206-2225.
  3. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04r, Department of Economics, University of Birmingham.
  4. Indrajit Ray & Sonali Gupta, 2013. "Coarse correlated equilibria in linear duopoly games," International Journal of Game Theory, Springer, vol. 42(2), pages 541-562, May.
  5. Julie Beugnot & Zeynep Gürgüç & Frederik Roose Øvlisen & Michael M. W. Roos, 2012. "Coordination failure caused by sunspots," Economics Bulletin, AccessEcon, vol. 32(4), pages 2860-2869.
  6. John Bone & Michalis Drouvelis & Indrajit Ray, 2012. "Following Recommendations to Avoid Coordination-Failure in 2 x 2 Games," Discussion Papers 12-04, Department of Economics, University of Birmingham.
  7. Guillén, Pablo & Hing, Alexander, 2013. "Lying through Their Teeth: Third Party Advice and Truth Telling in a Strategy Proof Mechanism," Working Papers 2013-11, University of Sydney, School of Economics.
  8. Indrajit Ray & Sonali Sen Gupta, 2012. "Coarse Correlated Equilibria and Sunspots," Discussion Papers 11-14r, Department of Economics, University of Birmingham.
  9. John Duffy & Ernest Lai & Wooyoung Lim, 2013. "Language and Coordination: An Experimental Study," Working Papers 514, University of Pittsburgh, Department of Economics, revised Dec 2013.

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