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An extension of quasi-hyperbolic discounting to continuous time

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  • Pan, Jinrui
  • Webb, Craig S.
  • Zank, Horst

Abstract

Two-Stage Exponential (TSE) discounting, the model developed here, generalises exponential discounting in a parsimonious way. It can be seen as an extension of Quasi-Hyperbolic discounting to continuous time. A TSE discounter has a constant rate of time preference before and after some threshold time; the switch point. If the switch point is expressed in calendar time, TSE discounting captures time consistent behaviour. If it is expressed in waiting time, TSE discounting captures time invariant behaviour. We provide preference foundations for all cases, showing how the switch point is derived endogenously from behaviour. We apply each case to Rubinstein's infinite-horizon, alternating-offers bargaining model.

Suggested Citation

  • Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
    • Handle: RePEc:eee:gamebe:v:89:y:2015:i:c:p:43-55
    DOI: 10.1016/j.geb.2014.11.003
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    3. Akin, Zafer & Yavas, Abdullah, 2023. "Elicited Time Preferences and Behavior in Long-Run Projects," MPRA Paper 117133, University Library of Munich, Germany.
    4. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    5. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    6. 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.
    7. Pavlo R. Blavatskyy, 2022. "Intertemporal choice as a tradeoff between cumulative payoff and average delay," Journal of Risk and Uncertainty, Springer, vol. 64(1), pages 89-107, February.
    8. Doruk Cetemen & Felix Zhiyu Feng & Can Urgun, 2019. "Contracting with Non-Exponential Discounting: Moral Hazard and Dynamic Inconsistency," Working Papers 2019-17, Princeton University. Economics Department..
    9. Blavatskyy, Pavlo, 2018. "Fechner’s strong utility model for choice among n>2 alternatives: Risky lotteries, Savage acts, and intertemporal payoffs," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 75-82.
    10. 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.
    11. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.
    12. Cui, Xiangyu & Li, Duan & Shi, Yun, 2020. "Resolving Time Inconsistency of Decision Problem with Non-expectation Operator: From Internal Conflict to Internal Harmony by Strategy of Self-Coordination," SocArXiv 8m5w2, Center for Open Science.
    13. Abdellaoui, Mohammed & Kemel, Emmanuel & Panin, Amma & Vieider, Ferdinand M., 2019. "Measuring time and risk preferences in an integrated framework," Games and Economic Behavior, Elsevier, vol. 115(C), pages 459-469.
    14. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.
    15. Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    16. Shou Chen & Richard Fu & Lei Wedge & Ziran Zou, 2019. "Non-hyperbolic discounting and dynamic preference reversal," Theory and Decision, Springer, vol. 86(2), pages 283-302, March.
    17. Craig S. Webb, 2019. "Trichotomic discounted utility," Theory and Decision, Springer, vol. 87(3), pages 321-339, October.
    18. 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.
    19. Jeongbin Kim & Wooyoung Lim & Sebastian Schweighofer-Kodritsch, 2023. "Patience Is Power: Bargaining and Payoff Delay," Berlin School of Economics Discussion Papers 0015, Berlin School of Economics.
    20. 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.
    21. Anujit Chakraborty, 2021. "Present Bias," Econometrica, Econometric Society, vol. 89(4), pages 1921-1961, July.
    22. Pavlo R. Blavatskyy & Hela Maafi, 2020. "A new test of convexity–concavity of discount function," Theory and Decision, Springer, vol. 89(2), pages 121-136, September.
    23. Lu, Shih En, 2016. "Self-control and bargaining," Journal of Economic Theory, Elsevier, vol. 165(C), pages 390-413.

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    More about this item

    Keywords

    Discounting; Present bias; Decreasing impatience; Bargaining;
    All these keywords.

    JEL classification:

    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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