IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v45y2009i7-8p479-490.html
   My bibliography  Save this article

Stopping with anticipated regret

Author

Listed:
  • Hayashi, Takashi

Abstract

This paper analyzes a stopping problem where the decision maker is driven by anticipated ex-post regret. There are two sources of potential dynamic inconsistency, one is arrival of information and the other is changing choice opportunities over time--discarding the current stopping option may change how she stops the game in the future. First we consider a naive planner who prescribes a commitment solution, and illustrate the nature of the inconsistency problem. Then we consider a sophisticated planner who plays backward induction against her [`]successive selves'. The resolution of dynamic inconsistency does not in general allow the use of standard dynamic programming technique. We provide, however, a simple characterization of the backward induction strategy, which is given in a recursive formula. We also provide a behavioral implication, that larger indeterminacy of belief may lead to a more aggressive behavior, that is, continuing the gamble longer, which contrasts to the implication of ambiguity aversion.

Suggested Citation

  • Hayashi, Takashi, 2009. "Stopping with anticipated regret," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 479-490, July.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:479-490
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(09)00030-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    3. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    4. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    5. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    6. Takashi Hayashi, 2008. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," KIER Working Papers 659, Kyoto University, Institute of Economic Research.
    7. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    8. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    9. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    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. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    2. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    3. Kleinberg, Jon & Kleinberg, Robert & Oren, Sigal, 2022. "Optimal stopping with behaviorally biased agents: The role of loss aversion and changing reference points," Games and Economic Behavior, Elsevier, vol. 133(C), pages 282-299.
    4. Philipp Strack & Paul Viefers, 2021. "Too Proud to Stop: Regret in Dynamic Decisions," Journal of the European Economic Association, European Economic Association, vol. 19(1), pages 165-199.
    5. Alexei Parakhonyak & Anton Sobolev, 2015. "Non‐Reservation Price Equilibrium and Search without Priors," Economic Journal, Royal Economic Society, vol. 0(584), pages 887-909, May.
    6. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    7. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    8. Takashi Hayashi, 2011. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," Theory and Decision, Springer, vol. 70(4), pages 399-430, April.
    9. T. D. Pol & S. Gabbert & H.-P. Weikard & E. C. Ierland & E. M. T. Hendrix, 2017. "A Minimax Regret Analysis of Flood Risk Management Strategies Under Climate Change Uncertainty and Emerging Information," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(4), pages 1087-1109, December.
    10. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.

    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. Takashi Hayashi, 2008. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," KIER Working Papers 659, Kyoto University, Institute of Economic Research.
    2. Takashi Hayashi, 2011. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," Theory and Decision, Springer, vol. 70(4), pages 399-430, April.
    3. Joseph Halpern & Samantha Leung, 2015. "Weighted sets of probabilities and minimax weighted expected regret: a new approach for representing uncertainty and making decisions," Theory and Decision, Springer, vol. 79(3), pages 415-450, November.
    4. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    5. Lorenzo Bastianello & José Heleno Faro, 2023. "Choquet expected discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May.
    6. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    7. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    8. Riella, Gil, 2013. "Preference for Flexibility and Dynamic Consistency," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2467-2482.
    9. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    10. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    11. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    12. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    13. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    14. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    15. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    16. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    17. Han Bleichrodt & Jurgen Eichberger & Simon Grant & David Kelsey & Chen Li, 2018. "A Test of Dynamic Consistency and Consequentialism in the Presence of Ambiguity," Discussion Papers 1803, University of Exeter, Department of Economics.
    18. Xiaoyu Cheng, 2020. "Ambiguous Persuasion: An Ex-Ante Formulation," Papers 2010.05376, arXiv.org, revised Nov 2023.
    19. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    20. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).

    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:eee:mateco:v:45:y:2009:i:7-8:p:479-490. See general information about how to correct material in RePEc.

    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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.