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Correlated Equilibrium, Public Signaling and Absorbing Games

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  • Eilon Solan
  • Rakesh V. Vohra

Abstract

An absorbing game is a repeated game where some of the action combinations are absorbing, in the sense that whenever they are played, there is a positive probability that the game terminates, and the players receive some terminal payoff at every future stage. We prove that every n-player absorbing game admits a correlated equilibrium. In other words, for every epsilon>0 there exits a probability distribution p (epsilon subscript) over the space of pure strategy profiles such that if a pure strategy profile is chosen according to p (epsilon subscript) and each player is informed of his pure strategy, no player can profit more than epsilon in any sufficiently long game by deviating from the recommended strategy.

Suggested Citation

  • Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1272
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
    3. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    4. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 43, pages 1665-1686, Elsevier.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Solan, Eilon, 2000. "Absorbing Team Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 245-261, May.
    8. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    9. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 303-314.
    11. 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. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "The MaxMin value of stochastic games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 133-150, December.

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