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Subgame Perfect Equilibria in Continuous-Time Repeated Games

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  • Mitri Kitti

    (University of Turku)

Abstract

This paper considers subgame perfect equilibria of continuous-time repeated games with perfect monitoring when immediate reactions to deviations are allowed. The set of subgame perfect equilibrium payoffs is shown to be a fixed-point of a set-valued operator introduced in the paper. For a large class of discrete time games the closure of this set corresponds to the limit payoffs of when the discount factors converge to one. It is shown that in the continuous-time setup pure strategies are sufficient for obtaining all equilibrium payoffs supported by the players' minimax values. Moreover, the equilibrium payoff set is convex and satisfies monotone comparative statics when the ratios of players' discount rates increase.

Suggested Citation

  • Mitri Kitti, 2018. "Subgame Perfect Equilibria in Continuous-Time Repeated Games," Discussion Papers 120, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp120
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    File URL: http://ace-economics.fi/kuvat/dp120.pdf
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    References listed on IDEAS

    as
    1. 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..
    2. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    3. James Bergin, 2006. "The folk theorem revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 321-332, January.
    4. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39, World Scientific Publishing Co. Pte. Ltd..
    5. Bergin, James, 1992. "A model of strategic behaviour in repeated games," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 113-153.
    6. Stinchcombe, Maxwell B., 1992. "Maximal strategy sets for continuous-time game theory," Journal of Economic Theory, Elsevier, vol. 56(2), pages 235-265, April.
    7. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    8. 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.
    9. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.
    10. Chen, Bo & Takahashi, Satoru, 2012. "A folk theorem for repeated games with unequal discounting," Games and Economic Behavior, Elsevier, vol. 76(2), pages 571-581.
    11. Murto, Pauli & Välimäki, Juuso, 2013. "Delay and information aggregation in stopping games with private information," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2404-2435.
    12. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    13. Mitri Kitti, 2013. "Conditional Markov equilibria in discounted dynamic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 77-100, August.
    14. ,, 2015. "Characterizing the limit set of PPE payoffs with unequal discounting," Theoretical Economics, Econometric Society, vol. 10(3), September.
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    More about this item

    Keywords

    repeated game; continuous time; subgame perfection; equilibrium payoff set;
    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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