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Coalition-Proof Correlated Equilibrium : A Definition

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  • RAY , Indrajit

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

We refine the notion of correlated equilibrium capturing the essence of coalition-proof Nash equilibrium concept. We define coalition-proof correlated equilibrium of a game as a pair consisting of a correlation device and a coalition-proof Nash equilibrium of the game extended by the correlation device. A direct coalition-proof correlated equilibrium is a canonical device such that the obedient strategy is a coalition-proof Nash equilibrium of the canonical extended game. The "revelation principle" does not hold. Even in case of two-person games, there exists coalition-proof correlated equilibrium for which the corresponding induced distribution is not a direct coalition-proof correlated equilibrium. The set of direct coalition-proof correlated equilibria is not convex unlike the set of correlated equilibria. For any game, a (pure) coalition-proof Nash equilibrium is always a direct coalition-proof correlated equilibrium. We compare our notion with other existing concepts through several examples.

Suggested Citation

  • RAY , Indrajit, 1993. "Coalition-Proof Correlated Equilibrium : A Definition," LIDAM Discussion Papers CORE 1993053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1993053
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    Cited by:

    1. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
    2. Giraud, Gael & Rochon, Celine, 2002. "Consistent collusion-proofness and correlation in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 441-463, December.
    3. Moreno, Diego & Wooders, John, 1996. "Coalition-Proof Equilibrium," Games and Economic Behavior, Elsevier, vol. 17(1), pages 80-112, November.
    4. Heller, Yuval, 2010. "Minority-proof cheap-talk protocol," Games and Economic Behavior, Elsevier, vol. 69(2), pages 394-400, July.
    5. Luo, Xiao, 2001. "General systems and [phiv]-stable sets -- a formal analysis of socioeconomic environments," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 95-109, November.
    6. Moreno, Diego & Wooders, John, 1998. "An Experimental Study of Communication and Coordination in Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 47-76, July.
    7. Ray, Indrajit, 1996. "Efficiency in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 32(3), pages 157-178, December.
    8. Bloch, Francis & Dutta, Bhaskar, 2009. "Correlated equilibria, incomplete information and coalitional deviations," Games and Economic Behavior, Elsevier, vol. 66(2), pages 721-728, July.
    9. Ohnishi, Kazuhiro, 2018. "Non-Altruistic Equilibria," MPRA Paper 88347, University Library of Munich, Germany.
    10. Heller, Yuval, 2008. "Ex-ante and ex-post strong correlated equilbrium," MPRA Paper 7717, University Library of Munich, Germany, revised 11 Mar 2008.
    11. Jobst Heitzig & Forest Simmons, 2012. "Some chance for consensus: voting methods for which consensus is an equilibrium," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 43-57, January.
    12. Gad Allon & Achal Bassamboo & Eren B. Çil, 2012. "Large-Scale Service Marketplaces: The Role of the Moderating Firm," Management Science, INFORMS, vol. 58(10), pages 1854-1872, October.
    13. Kukushkin, Nikolai S., 1997. "An existence result for coalition-proof equilibrium," Economics Letters, Elsevier, vol. 57(3), pages 269-273, December.
    14. Grandjean, Gilles & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Communication structure and coalition-proofness – Experimental evidence," European Economic Review, Elsevier, vol. 94(C), pages 90-102.
    15. Heller, Yuval, 2010. "All-stage strong correlated equilibrium," Games and Economic Behavior, Elsevier, vol. 69(1), pages 184-188, May.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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