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Equilibrium Paths in Discounted Supergames

Author

Listed:
  • Kimmo Berg

    (Systems Analysis Laboratory, Aalto University School of Science)

  • Mitri Kitti

    (Department of Economics, University of Turku)

Abstract

This paper characterizes the subgame-perfect pure-strategy equilibrium paths in discounted supergames with perfect monitoring. It is shown that all the equilibrium paths are composed of fragments called elementary subpaths. This characterization result is complemented with an algorithm for finding the elementary subpaths. By using these subpaths it is possible to generate equilibrium paths and payoffs. When there are finitely many elementary subpaths, all the equilibrium paths can be represented by a directed graph. These graphs can be used in analyzing the complexity of equilibrium outcomes. In particular, it is shown that the size and the density of the equilibrium set can be measured by the asymptotic growth rate of equilibrium paths and the Hausdorff dimension of the payoff set.

Suggested Citation

  • Kimmo Berg & Mitri Kitti, 2014. "Equilibrium Paths in Discounted Supergames," Discussion Papers 96, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp96
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    File URL: http://www.mitrikitti.fi/dp96.pdf
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    References listed on IDEAS

    as
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    3. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    4. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    5. Kimmo Berg & Mitri Kitti, 2013. "Computing Equilibria in Discounted 2 × 2 Supergames," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 71-88, January.
    6. Salonen, Hannu & Vartiainen, Hannu, 2008. "Valuating payoff streams under unequal discount factors," Economics Letters, Elsevier, vol. 99(3), pages 595-598, June.
    7. Mailath, George J. & Obara, Ichiro & Sekiguchi, Tadashi, 2002. "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 40(1), pages 99-122, July.
    8. Sorin, Sylvain, 1992. "Repeated games with complete 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 1, chapter 4, pages 71-107, Elsevier.
    9. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    10. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    11. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
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    Cited by:

    1. Jörn Künsemöller & Nan Zhang & Kimmo Berg & João Soares, 2017. "A game-theoretic evaluation of an ISP business model in caching," Information Systems Frontiers, Springer, vol. 19(4), pages 803-818, August.
    2. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.
    3. Jörn Künsemöller & Nan Zhang & Kimmo Berg & João Soares, 0. "A game-theoretic evaluation of an ISP business model in caching," Information Systems Frontiers, Springer, vol. 0, pages 1-16.

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    More about this item

    Keywords

    repeated game; subgame-perfect equilibrium; equilibrium path; graph presentation of paths; complexity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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