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On the feasible payoff set of two-player repeated games with unequal discounting

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  • Bo Chen
  • Satoru Fujishige

Abstract

We provide a novel characterization of the feasible payoff set of a general two-player repeated game with unequal discounting. In particular, we show that generically the Pareto frontier shifts outwards and the feasible payoff set expands in the sense of set inclusion, as the time horizon increases. This result reinforces and refines the insight in Lehrer and Pauzner ( 1999 ) by showing that a longer horizon enables the players to conduct intertemporal trade in a more flexible fashion. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:295-303
    DOI: 10.1007/s00182-012-0354-6
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    References listed on IDEAS

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    1. Gonzalez-Diaz, Julio, 2006. "Finitely repeated games: A generalized Nash folk theorem," Games and Economic Behavior, Elsevier, vol. 55(1), pages 100-111, April.
    2. Wojciech Olszewski, 1998. "Note Perfect folk theorems. Does public randomization matter?," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 147-156.
    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. Salonen, Hannu & Vartiainen, Hannu, 2008. "Valuating payoff streams under unequal discount factors," Economics Letters, Elsevier, vol. 99(3), pages 595-598, June.
    5. Chen, Bo, 2007. "The Pareto frontier of a finitely repeated game with unequal discounting," Economics Letters, Elsevier, vol. 94(2), pages 177-184, February.
    6. Smith, Lones, 1995. "Necessary and Sufficient Conditions for the Perfect Finite Horizon Folk Theorem," Econometrica, Econometric Society, vol. 63(2), pages 425-430, March.
    7. Gossner, Olivier, 1995. "The Folk Theorem for Finitely Repeated Games with Mixed Strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 95-107.
    8. 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.
    9. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    10. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
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    Cited by:

    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. Daehyun Kim & Chihiro Morooka, 2023. "Characterizing the Feasible Payoff Set of OLG Repeated Games," Papers 2303.12988, arXiv.org, revised Feb 2024.

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    More about this item

    Keywords

    Intertemporal trade; Feasible payoff set; repeated game; unequal discounting; C70; C72; C73;
    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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