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Equilibrium payoffs in two-player discounted OLG games

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  • Chihiro Morooka

    (The University of Tokyo)

Abstract

This paper studies payoffs in subgame perfect equilibria of two-player discounted overlapping generations games with perfect monitoring. Assuming that mixed strategies are observable and a public randomization device is available, it is shown that sufficiently patient players can obtain any payoffs in the interior of the smallest rectangle containing the feasible and strictly individually rational payoffs of the stage game, when we first choose the rate of discount and then choose the players’ lifespan. Unlike repeated games without overlapping generations, obtaining payoffs outside the feasible set of the stage game does not require unequal discounting.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:4:d:10.1007_s00182-021-00779-9
    DOI: 10.1007/s00182-021-00779-9
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    References listed on IDEAS

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    1. 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.
    2. 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..
    3. 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.
    4. 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.
    5. 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.
    6. Michihiro Kandori, 1992. "Repeated Games Played by Overlapping Generations of Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 81-92.
    7. Smith, Lones, 1992. "Folk theorems in overlapping generations games," Games and Economic Behavior, Elsevier, vol. 4(3), pages 426-449, July.
    8. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
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    Cited by:

    1. Morooka, Chihiro, 2021. "Overlapping generations games with growing payoffs," Economics Letters, Elsevier, vol. 207(C).
    2. Daehyun Kim & Chihiro Morooka, 2023. "Characterizing the Feasible Payoff Set of OLG Repeated Games," Papers 2303.12988, arXiv.org, revised Dec 2024.

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    More about this item

    Keywords

    Overlapping generations games; Intertemporal trade; Discounted games; Folk theorem; Rectangular hull;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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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