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Repeated Games Without Public Randomization: A Constructive Approach

Author

Listed:
  • Ani Dasgupta

    (International Maritime Business Department, Massachusetts Maritime Academy and Economics Department, Boston University.)

  • Sambuddha Ghosh

    (Economics Group, Shanghai University of Finance and Economics)

Abstract

We study discounted infinitely repeated games with perfect monitoring and without public randomization. Both symmetric and asymmetric discounting cases are considered; a new geometric construct called ‘self-accessibility’ is proposed and used to unify the analyses of these two cases. For symmetric discounting, our approach leads to easy computability of a discount factor bound needed to support a specific payoff vector in equilibrium. When discounting is allowed to be asymmetric, we show that any payoff vector that is in the interior of the smallest rectangular region containing the pureaction payoffs is realizable in the repeated game. Next, an easily-verifiable condition, ‘strict diagonalizability’, is offered as a sufficient and almost necessary condition for a payoff vector to be an equilibrium payoff for some discount factor vector. ‘Turnpike strategies’ that support a target payoff are explicitly constructed. Our results thus encompass and generalize Fudenberg and Maskin (1986, 1991).

Suggested Citation

  • Ani Dasgupta & Sambuddha Ghosh, 2017. "Repeated Games Without Public Randomization: A Constructive Approach," Boston University - Department of Economics - Working Papers Series WP2017-011, Boston University - Department of Economics, revised Feb 2019.
    • Handle: RePEc:bos:wpaper:wp2017-011
    as

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    File URL: http://www.bu.edu/econ/files/2019/02/PRD_AD_2019_v4.pdf
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    References listed on IDEAS

    as
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    2. Bo Chen & Satoru Fujishige, 2013. "On the feasible payoff set of two-player repeated games with unequal discounting," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 295-303, February.
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    8. Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    9. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
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    11. 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.
    12. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
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    14. Yuichi Yamamoto, 2010. "The use of public randomization in discounted repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 431-443, July.
    15. ,, 2015. "Characterizing the limit set of PPE payoffs with unequal discounting," Theoretical Economics, Econometric Society, vol. 10(3), September.
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    Cited by:

    1. Chihiro Morooka, 2021. "Equilibrium payoffs in two-player discounted OLG games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 1021-1032, December.
    2. Chihiro Morooka, 2022. "A New Folk Theorem in OLG Games," CIRJE F-Series CIRJE-F-1203, CIRJE, Faculty of Economics, University of Tokyo.
    3. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).

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    Keywords

    ambiguity; Repeated Games; Public Randomization; Asymmetric Discounting;
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