IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/22342.html
   My bibliography  Save this paper

Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles

Author

Listed:
  • Cadogan, Godfrey

Abstract

We augment Tversky and Khaneman (1992) (“TK92”) Cumulative Prospect Theory (“CPT”) function space with a sample space for “states of nature”, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral stochastic processes arising from deformation of stochastic choice into outcome. A psychological distance metric (in the class of Dudley-Talagrand inequalities) popularized by Norman (1968); Nosofsky and Palmeri (1997), for stochastic learning, was used to characterize stopping times for behavioral processes. In which case, for a class of nonseparable space-time probability density functions, based on psychological distance, and independently proposed by Baucells and Heukamp (2009), we find that behavioral processes are uniformly stopped before the goal of fair gamble is attained. Further, we find that when faced with a fair gamble, agents exhibit submartingale [supermartingale] behavior, subjectively, under CPT probability weighting scheme. We show that even when agents’ have classic von Neuman-Morgenstern preferences over probability distribution, and know that the gamble is a martingale, they exhibit probability weighting to compensate for probability leakage arising from the their stopped behavioral process.

Suggested Citation

  • Cadogan, Godfrey, 2010. "Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles," MPRA Paper 22342, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:22342
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/22342/1/MPRA_paper_22342.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/22351/1/MPRA_paper_22351.pdf
    File Function: revised version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/22388/1/MPRA_paper_22388.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
    3. Massa, Massimo & Simonov, Andrei, 2005. "Is learning a dimension of risk?," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2605-2632, October.
    4. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    5. Steinbacher, Matjaz, 2008. "Stochastic Processes in Finance and Behavioral Finance," MPRA Paper 13603, University Library of Munich, Germany.
    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. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    2. David Bruner, 2009. "Changing the probability versus changing the reward," Experimental Economics, Springer;Economic Science Association, vol. 12(4), pages 367-385, December.
    3. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    4. Cadogan, Godfrey, 2010. "Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures," MPRA Paper 22380, University Library of Munich, Germany.
    5. Shi, Yun & Cui, Xiangyu & Zhou, Xunyu, 2020. "Beta and Coskewness Pricing: Perspective from Probability Weighting," SocArXiv 5rqhv, Center for Open Science.
    6. Alex Stomper & Marie-Louise Vierø, 2015. "Iterated Expectations Under Rank-dependent Expected Utility And Model Consistency," Working Paper 1228, Economics Department, Queen's University.
    7. Filiz-Ozbay, Emel & Guryan, Jonathan & Hyndman, Kyle & Kearney, Melissa & Ozbay, Erkut Y., 2015. "Do lottery payments induce savings behavior? Evidence from the lab," Journal of Public Economics, Elsevier, vol. 126(C), pages 1-24.
    8. Alarie, Yves & Dionne, Georges, 2005. "Testing explanations of preference reversal: A model," Working Papers 05-2, HEC Montreal, Canada Research Chair in Risk Management.
    9. 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.
    10. Foster, Gigi & Frijters, Paul & Schaffner, Markus & Torgler, Benno, 2018. "Expectation formation in an evolving game of uncertainty: New experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 379-405.
    11. Daniel Woods & Mustafa Abdallah & Saurabh Bagchi & Shreyas Sundaram & Timothy Cason, 2022. "Network defense and behavioral biases: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 254-286, February.
    12. Che-Yuan Liang, 2017. "Optimal inequality behind the veil of ignorance," Theory and Decision, Springer, vol. 83(3), pages 431-455, October.
    13. 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.
    14. 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.
    15. 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.
    16. Bocqueho, Geraldine & Jacquet, Florence & Reynaud, Arnaud, 2011. "Expected Utility or Prospect Theory Maximizers? Results from a Structural Model based on Field-experiment Data," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114257, European Association of Agricultural Economists.
    17. Philip Bromiley, 2009. "A Prospect Theory Model of Resource Allocation," Decision Analysis, INFORMS, vol. 6(3), pages 124-138, September.
    18. Freudenreich, Hanna & Musshoff, Oliver & Wiercinski, Ben, 2017. "The Relationship between Farmers' Shock Experiences and their Uncertainty Preferences - Experimental Evidence from Mexico," GlobalFood Discussion Papers 256212, Georg-August-Universitaet Goettingen, GlobalFood, Department of Agricultural Economics and Rural Development.
    19. Syngjoo Choi & Jeongbin Kim & Eungik Lee & Jungmin Lee, 2022. "Probability Weighting and Cognitive Ability," Management Science, INFORMS, vol. 68(7), pages 5201-5215, July.
    20. Luis Sarmiento, 2020. "I Am Innocent: Hourly Variations in Air Pollution and Crime Behavior," Discussion Papers of DIW Berlin 1879, DIW Berlin, German Institute for Economic Research.

    More about this item

    Keywords

    commutative prospect theory; homotopy; stopping time; behavioral stochastic process;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:pra:mprapa:22342. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.