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Stopping with anticipated regret

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  • 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
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    References listed on IDEAS

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    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    3. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    4. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    5. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    6. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    7. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    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. 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.
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    Cited by:

    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    3. 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.
    4. 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.
    5. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    6. repec:kap:enreec:v:68:y:2017:i:4:d:10.1007_s10640-016-0062-y is not listed on IDEAS
    7. Paul Viefers & Philipp Strack, 2014. "Too Proud to Stop: Regret in Dynamic Decisions," Discussion Papers of DIW Berlin 1401, DIW Berlin, German Institute for Economic Research.

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