IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.03157.html
   My bibliography  Save this paper

When to Quit Gambling, if You Must!

Author

Listed:
  • Sang Hu
  • Jan Obloj
  • Xun Yu Zhou

Abstract

We develop an approach to solve Barberis (2012)'s casino gambling model in which a gambler whose preferences are specified by the cumulative prospect theory (CPT) must decide when to stop gambling by a prescribed deadline. We assume that the gambler can assist their decision using an independent randomization, and explain why it is a reasonable assumption. The problem is inherently time-inconsistent due to the probability weighting in CPT, and we study both precommitted and naive stopping strategies. We turn the original problem into a computationally tractable mathematical program, based on which we derive an optimal precommitted rule which is randomized and Markovian. The analytical treatment enables us to make several predictions regarding a gambler's behavior, including that with randomization they may enter the casino even when allowed to play only once, that whether they will play longer once they are granted more bets depends on whether they are in a gain or at a loss, and that it is prevalent that a naivite never stops loss.

Suggested Citation

  • Sang Hu & Jan Obloj & Xun Yu Zhou, 2021. "When to Quit Gambling, if You Must!," Papers 2102.03157, arXiv.org.
    • Handle: RePEc:arx:papers:2102.03157
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.03157
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Enrico Diecidue & Ulrich Schmidt & Peter P. Wakker, 2004. "The Utility of Gambling Reconsidered," Journal of Risk and Uncertainty, Springer, vol. 29(3), pages 241-259, December.
    2. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Rubinstein, Ariel, 2002. "Irrational diversification in multiple decision problems," European Economic Review, Elsevier, vol. 46(8), pages 1369-1378, September.
    6. Henderson, Vicky & Hobson, David & Tse, Alex S.L., 2017. "Randomized strategies and prospect theory in a dynamic context," Journal of Economic Theory, Elsevier, vol. 168(C), pages 287-300.
    7. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    8. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    9. Gary E Bolton & Jordi Brandts & Axel Ockenfels, 2005. "Fair Procedures: Evidence from Games Involving Lotteries," Economic Journal, Royal Economic Society, vol. 115(506), pages 1054-1076, October.
    10. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    11. repec:bla:jfinan:v:53:y:1998:i:5:p:1775-1798 is not listed on IDEAS
    12. Sebastian Ebert & Philipp Strack, 2015. "Until the Bitter End: On Prospect Theory in a Dynamic Context," American Economic Review, American Economic Association, vol. 105(4), pages 1618-1633, April.
    13. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard, 1986. "Fairness as a Constraint on Profit Seeking: Entitlements in the Market," American Economic Review, American Economic Association, vol. 76(4), pages 728-741, September.
    14. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    Full references (including those not matched with items on IDEAS)

    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. Dwenger, Nadja & Kübler, Dorothea & Weizsäcker, Georg, 2018. "Flipping a coin: Evidence from university applications," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 167, pages 240-250.
    2. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    3. Dwenger, Nadja & Kübler, Dorothea & Weizsäcker, Georg, 2014. "Flipping a coin: Theory and evidence," Discussion Papers, Research Unit: Market Behavior SP II 2013-201r, WZB Berlin Social Science Center.
    4. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    5. Sang Hu & Jan Obłój & Xun Yu Zhou, 2023. "A Casino Gambling Model Under Cumulative Prospect Theory: Analysis and Algorithm," Management Science, INFORMS, vol. 69(4), pages 2474-2496, April.
    6. Henderson, Vicky & Hobson, David & Tse, Alex S.L., 2018. "Probability weighting, stop-loss and the disposition effect," Journal of Economic Theory, Elsevier, vol. 178(C), pages 360-397.
    7. Markus Dertwinkel-Kalt & Jonas Frey, 2020. "Optimal Stopping in a Dynamic Salience Model," CESifo Working Paper Series 8496, CESifo.
    8. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    9. Rawley Heimer & Zwetelina Iliewa & Alex Imax & Martin Weber, 2021. "Dynamic Inconsistency in Risky Choice: Evidence from the Lab and Field," ECONtribute Discussion Papers Series 094, University of Bonn and University of Cologne, Germany.
    10. Markus Dertwinkel‐Kalt & Jonas Frey, 2024. "Optimal Stopping In A Dynamic Salience Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 65(2), pages 885-913, May.
    11. Vicky Henderson & Jonathan Muscat, 2020. "Partial liquidation under reference-dependent preferences," Finance and Stochastics, Springer, vol. 24(2), pages 335-357, April.
    12. Chew, Soo Hong & Miao, Bin & Shen, Qiang & Zhong, Songfa, 2022. "Multiple-switching behavior in choice-list elicitation of risk preference," Journal of Economic Theory, Elsevier, vol. 204(C).
    13. Embrey, Matthew & Seel, Christian & Philipp Reiss, J., 2024. "Gambling in risk-taking contests: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 221(C), pages 570-585.
    14. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    15. Henderson, Vicky & Hobson, David & Tse, Alex S.L., 2017. "Randomized strategies and prospect theory in a dynamic context," Journal of Economic Theory, Elsevier, vol. 168(C), pages 287-300.
    16. Voraprapa Nakavachara & Roongkiat Ratanabanchuen & Kanis Saengchote & Thitiphong Amonthumniyom & Pongsathon Parinyavuttichai & Polpatt Vinaibodee, 2023. "Do People Gamble or Invest in the Cryptocurrency Market? Transactional-Level Evidence from Thailand," PIER Discussion Papers 206, Puey Ungphakorn Institute for Economic Research, revised Feb 2024.
    17. Pavlo R. Blavatskyy & Francesco Feri, 2018. "Violations of betweenness and choice shifts in groups," Theory and Decision, Springer, vol. 85(3), pages 321-331, October.
    18. Dwenger, Nadja & Kübler, Dorothea & Weizsäcker, Georg, 2013. "Preference for randomization: Empirical and experimental evidence," SFB 649 Discussion Papers 2013-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Ebert, Sebastian & Hilpert, Christian, 2019. "Skewness preference and the popularity of technical analysis," Journal of Banking & Finance, Elsevier, vol. 109(C).
    20. Brice Corgnet & Roberto Hernán González, 2023. "On The Appeal Of Complexity," Working Papers 2312, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.

    More about this item

    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:arx:papers:2102.03157. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.