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A Casino Gambling Model Under Cumulative Prospect Theory: Analysis and Algorithm

Author

Listed:
  • Sang Hu

    (School of Data Science, Chinese University of Hong Kong, Shenzhen 518172, China)

  • Jan Obłój

    (Mathematical Institute, Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford OX2 6ED, United Kingdom; St John’s College, Oxford OX1 3JP, United Kingdom)

  • Xun Yu Zhou

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

Abstract

We develop an approach to solve the Barberis casino gambling model [Barberis N (2012) A model of casino gambling. Management Sci. 58(1):35–51] 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 independent randomization. The problem is inherently time inconsistent because of the probability weighting in CPT, and we study both precommitted and naïve stopping strategies. We turn the original problem into a computationally tractable mathematical program from which we devise an algorithm to compute optimal precommitted rules that are randomized and Markovian. The analytical treatment enables us to confirm the economic insights of Barberis for much longer time horizons and to make additional predictions regarding a gambler’s behavior, including that, with randomization, a gambler may enter the casino even when allowed to play only once and that it is prevalent that a naïf never stops loss.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:4:p:2474-2496
    DOI: 10.1287/mnsc.2022.4414
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    References listed on IDEAS

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    1. 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.
    2. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    3. 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.
    4. Terrance Odean, 1998. "Are Investors Reluctant to Realize Their Losses?," Journal of Finance, American Finance Association, vol. 53(5), pages 1775-1798, October.
    5. 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.
    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. 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.
    8. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    9. 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.
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