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Correlated equilibrium payoffs and public signalling in absorbing games

Author

Listed:
  • Eilon Solan

    (Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, and School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel)

  • Rakesh V. Vohra

    (Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston IL 60208)

Abstract

An absorbing game is a repeated game where some 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 multi-player absorbing game admits a correlated equilibrium payoff. In other words, for every >0 there exists a probability distribution p over the space of pure strategy profiles that satisfies the following. With probability at least 1-, if a pure strategy profile is chosen according to p and each player is informed of his pure strategy, no player can profit more than in any sufficiently long game by deviating from the recommended strategy.

Suggested Citation

  • Eilon Solan & Rakesh V. Vohra, 2002. "Correlated equilibrium payoffs and public signalling in absorbing games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 91-121.
    • Handle: RePEc:spr:jogath:v:31:y:2002:i:1:p:91-121
    Note: Received: April 2001/Revised: June 4, 2002
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    Citations

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    Cited by:

    1. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.
    2. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    3. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2009. "Stochastic games on a product state space: the periodic case," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 263-289, June.
    4. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.
    5. Alejandro Lee-Penagos, 2016. "Learning to Coordinate: Co-Evolution and Correlated Equilibrium," Discussion Papers 2016-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    6. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    7. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    8. Eilon Solan, 2002. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Discussion Papers 1356, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Stochastic games on a product state space: the periodic case," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2008. "Stochastic Games on a Product State Space," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 403-420, May.
    11. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    12. Eilon Solan & Omri N. Solan, 2021. "Sunspot equilibrium in positive recursive general quitting games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 891-909, December.
    13. Yuval Heller, 2012. "Sequential Correlated Equilibria in Stopping Games," Operations Research, INFORMS, vol. 60(1), pages 209-224, February.
    14. Eilon Solan, 2018. "The modified stochastic game," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1287-1327, November.
    15. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.

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