IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v65y2017i1p97-103.html
   My bibliography  Save this article

Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model

Author

Listed:
  • Xue Dong He

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong)

  • Sang Hu

    (School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China)

  • Jan Obłój

    (Mathematical Institute, Oxford-Man Institute of Quantitative Finance and St John’s College, University of Oxford, Oxford OX2 6GG, United Kingdom)

  • Xun Yu Zhou

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:1:p:97-103
    DOI: 10.1287/opre.2016.1545
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2016.1545
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1545?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. 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.
    3. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    5. 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.
    6. 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..
    7. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    8. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
    9. Richard H. Thaler & Eric J. Johnson, 1990. "Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice," Management Science, INFORMS, vol. 36(6), pages 643-660, June.
    10. 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.
    11. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    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. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    2. Vicky Henderson & David Hobson & Matthew Zeng, 2023. "Cautious stochastic choice, optimal stopping and deliberate randomization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 887-922, April.

    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. 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.
    2. 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.
    3. 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.
    4. Arjan Verschoor & Ben D’Exelle, 2022. "Probability weighting for losses and for gains among smallholder farmers in Uganda," Theory and Decision, Springer, vol. 92(1), pages 223-258, February.
    5. Eyal Baharad & Doron Kliger, 2013. "Market failure in light of non-expected utility," Theory and Decision, Springer, vol. 75(4), pages 599-619, October.
    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. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    8. 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.
    9. M. Pelé & M. Broihanne & B. Thierry & J. Call & V. Dufour, 2014. "To bet or not to bet? Decision-making under risk in non-human primates," Journal of Risk and Uncertainty, Springer, vol. 49(2), pages 141-166, October.
    10. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    11. George Wu & Alex B. Markle, 2008. "An Empirical Test of Gain-Loss Separability in Prospect Theory," Management Science, INFORMS, vol. 54(7), pages 1322-1335, July.
    12. José Lara Resende & George Wu, 2010. "Competence effects for choices involving gains and losses," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 109-132, April.
    13. Phillips Peter J. & Pohl Gabriela, 2018. "The Deferral of Attacks: SP/A Theory as a Model of Terrorist Choice when Losses Are Inevitable," Open Economics, De Gruyter, vol. 1(1), pages 71-85, February.
    14. Mickael Beaud & Marc Willinger, 2015. "Are People Risk Vulnerable?," Management Science, INFORMS, vol. 61(3), pages 624-636, March.
    15. Sang Hu & Jan Obloj & Xun Yu Zhou, 2021. "When to Quit Gambling, if You Must!," Papers 2102.03157, arXiv.org.
    16. Kliger, Doron & Levy, Ori, 2009. "Theories of choice under risk: Insights from financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 330-346, August.
    17. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    18. Ariane Charpin, 2018. "Tests des modèles de décision en situation de risque. Le cas des parieurs hippiques en France," Revue économique, Presses de Sciences-Po, vol. 69(5), pages 779-803.
    19. Markus Dertwinkel-Kalt & Jonas Frey, 2020. "Optimal Stopping in a Dynamic Salience Model," CESifo Working Paper Series 8496, CESifo.
    20. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2014. "Dual criteria decisions," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 101-113.
      • Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet, 2009. "Dual Criteria Decisions," Working Papers 02-2009, Copenhagen Business School, Department of Economics.

    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:inm:oropre:v:65:y:2017:i:1:p:97-103. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.