IDEAS home Printed from https://ideas.repec.org/p/yon/wpaper/2015rwp-84.html
   My bibliography  Save this paper

Repeated Games with General Discounting

Author

Listed:
  • Ichiro Obara

    (University of California)

  • Jaeok Park

    (Yonsei University)

Abstract

We introduce a general class of time discounting, which includes time-inconsistent ones, into repeated games with perfect monitoring. A strategy pro le is called an agent subgame perfect equilibrium if there is no pro table one-shot deviation at any history. We characterize strongly symmetric agent subgame perfect equilibria for repeated games with symmetric stage game. We nd that the harshest punishment takes different forms given different biases. When players are future biased, the harshest punishment is supported by a version of stick-and-carrot strategy. When players are present biased, the harshest punishment may take a more complex form. In particular, the worst punishment path may need to be cyclical. We also nd that the worst punishment payoff is different from the stage game minmax payoff even when players are patient. For some class of discounting, we show that the worst punishment payoff is larger than the stage game minmax payoff with present bias and smaller than the stage game minmax payo with future bias. We also characterize the set of limit equilibrium payoffs as the length of periods converges to 0, without changing the intertemporal structure of biases.

Suggested Citation

  • Ichiro Obara & Jaeok Park, 2015. "Repeated Games with General Discounting," Working papers 2015rwp-84, Yonsei University, Yonsei Economics Research Institute.
  • Handle: RePEc:yon:wpaper:2015rwp-84
    as

    Download full text from publisher

    File URL: ftp://165.132.78.176/repec/yon/wpaper/2015rwp-84.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    2. Laibson, David, 1998. "Life-cycle consumption and hyperbolic discount functions," European Economic Review, Elsevier, vol. 42(3-5), pages 861-871, May.
    3. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
    4. S. Dellavigna., 2011. "Psychology and Economics: Evidence from the Field," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 4.
    5. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    6. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non‐stationary Time Preference and “Hyperbolic” Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    7. Chade, Hector & Prokopovych, Pavlo & Smith, Lones, 2008. "Repeated games with present-biased preferences," Journal of Economic Theory, Elsevier, vol. 139(1), pages 157-175, March.
    8. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    9. Katsutoshi Wakai, 2008. "A Model of Utility Smoothing," Econometrica, Econometric Society, vol. 76(1), pages 137-153, January.
    10. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    11. Takeuchi, Kan, 2011. "Non-parametric test of time consistency: Present bias and future bias," Games and Economic Behavior, Elsevier, vol. 71(2), pages 456-478, March.
    12. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1449-1499.
    13. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    14. Loewenstein, George, 1987. "Anticipation and the Valuation of Delayed Consumption," Economic Journal, Royal Economic Society, vol. 97(387), pages 666-684, September.
    15. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    16. 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.
    17. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    18. Tadashi Sekiguchi & Katsutoshi Wakai, 2016. "Repeated Games with Recursive Utility:Cournot Duopoly under Gain/Loss Asymmetry," Discussion papers e-16-006, Graduate School of Economics , Kyoto University.
    19. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    20. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    21. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    22. Serdar Sayman & Ayse Öncüler, 2009. "An Investigation of Time Inconsistency," Management Science, INFORMS, vol. 55(3), pages 470-482, March.
    23. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," Review of Economic Studies, Oxford University Press, vol. 4(2), pages 155-161.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernergård, Axel, 2019. "Self-control problems and the folk theorem," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 332-347.
    2. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    3. Kim, Jeongbin & Lim, Wooyoung & Schweighofer-Kodritsch, Sebastian, 2020. "Bargaining and Time Preferences: An Experimental Study," Rationality and Competition Discussion Paper Series 254, CRC TRR 190 Rationality and Competition.
    4. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    2. Han Bleichrodt & Yu Gao & Kirsten I. M. Rohde, 2016. "A measurement of decreasing impatience for health and money," Journal of Risk and Uncertainty, Springer, vol. 52(3), pages 213-231, June.
    3. Sebastian Schweighofer-Kodritsch, 2015. "Time Preferences and Bargaining," STICERD - Theoretical Economics Paper Series /2015/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Laurent Denant-Boemont & Enrico Diecidue & Olivier l’Haridon, 2017. "Patience and time consistency in collective decisions," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 181-208, March.
    5. Altınok, Ahmet & Yılmaz, Murat, 2018. "Dynamic voluntary contribution to a public project under time inconsistency," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 114-140.
    6. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    7. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    8. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.
    9. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(C).
    10. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    11. Nina Anchugina, 2017. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Theory and Decision, Springer, vol. 82(2), pages 185-210, February.
    12. Nina Anchugina, 2015. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Papers 1511.06454, arXiv.org.
    13. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    14. Shotaro Shiba & Kazumi Shimizu, 2017. "Does Time Inconsistency Differ between Gain and Loss? An Intra-Personal Comparison Using a Non-Parametric Designed Experimen," Working Papers 1714, Waseda University, Faculty of Political Science and Economics.
    15. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    16. Ubfal, Diego, 2016. "How general are time preferences? Eliciting good-specific discount rates," Journal of Development Economics, Elsevier, vol. 118(C), pages 150-170.
    17. Teck H. Ho & Noah Lim & Colin Camerer, 2005. "Modeling the Psychology of Consumer and Firm Behavior with Behavioral Economics," Levine's Bibliography 784828000000000476, UCLA Department of Economics.
    18. Murat Yilmaz, 2018. "An Extended Survey of Time-Inconsistency and Its Applications," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 32(1), pages 55-73.
    19. Minwook Kang, 2015. "Welfare criteria for quasi-hyperbolic time preferences," Economics Bulletin, AccessEcon, vol. 35(4), pages 2506-2511.
    20. Minwook Kang, 2019. "Pareto-improving tax policies under hyperbolic discounting," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 26(3), pages 618-660, June.

    More about this item

    Keywords

    Hyperbolic Discounting; Present Bias; Repeated Game; Time Inconsistency;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:yon:wpaper:2015rwp-84. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/eryonkr.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: YERI (email available below). General contact details of provider: https://edirc.repec.org/data/eryonkr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.