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Cumulative prospect theory and gambling

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  • M Cain
  • D Law
  • D Peel

Abstract

Whilst Cumulative Prospect theory (CPT) provides an explanation of gambling on longshots at actuarially unfair odds, it cannot explain why people might bet on more favoured outcomes. This paper shows that this is explicable if the degree of loss aversion experienced by the agent is reduced for small-stake gambles (as a proportion of wealth), and probability distortions are greater over losses than gains. If the utility or value function is assumed to be bounded, the degree of loss aversion assumed by Kahneman and Tversky leads to absurd predictions, reminiscent of those pointed out by Rabin (2000), of refusal to accept infinite gain bets at low probabilities. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum at low probabilities, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum. These implications are consistent with outcomes observed in gambling markets.

Suggested Citation

  • M Cain & D Law & D Peel, 2005. "Cumulative prospect theory and gambling," Working Papers 566823, Lancaster University Management School, Economics Department.
  • Handle: RePEc:lan:wpaper:566823
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    File URL: http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/working-papers/CumulativeProspectTheory.pdf
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    References listed on IDEAS

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    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.
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    5. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    6. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    7. 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.
    8. Matthew Rabin & Richard H. Thaler, 2001. "Anomalies: Risk Aversion," Journal of Economic Perspectives, American Economic Association, vol. 15(1), pages 219-232, Winter.
    9. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    10. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    11. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    12. Joseph Golec & Maurry Tamarkin, 1998. "Bettors Love Skewness, Not Risk, at the Horse Track," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 205-225, February.
    13. Vaughan Williams, Leighton, 1999. "Information Efficiency in Betting Markets: A Survey," Bulletin of Economic Research, Wiley Blackwell, vol. 51(1), pages 1-30, January.
    14. Conlisk, John, 1993. "The Utility of Gambling," Journal of Risk and Uncertainty, Springer, vol. 6(3), pages 255-275, June.
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    Cited by:

    1. Maschke Mario & Schmidt Ulrich, 2011. "Das Wettmonopol in Deutschland: Status quo und Reformansätze," Zeitschrift für Wirtschaftspolitik, De Gruyter, vol. 60(1), pages 110-124, April.
    2. repec:ebl:ecbull:v:4:y:2007:i:26:p:1-10 is not listed on IDEAS

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