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Optimal lottery

Author

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  • Dennery, Charles
  • Direr, Alexis

Abstract

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.

Suggested Citation

  • Dennery, Charles & Direr, Alexis, 2014. "Optimal lottery," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 15-23.
  • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:15-23
    DOI: 10.1016/j.jmateco.2014.09.011
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    References listed on IDEAS

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    1. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    2. repec:dau:papers:123456789/2348 is not listed on IDEAS
    3. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    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. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    6. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Harry M. Markowitz, 2010. "Portfolio Theory: As I Still See It," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 1-23, December.
    9. 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.
    10. Fennema, Hein & van Assen, Marcel, 1998. "Measuring the Utility of Losses by Means of the Tradeoff Method," Journal of Risk and Uncertainty, Springer, vol. 17(3), pages 277-295, December.
    11. Kent Grote & Victor Matheson, 2011. "The Economics of Lotteries: A Survey of the Literature," Working Papers 1109, College of the Holy Cross, Department of Economics.
    12. Erik Snowberg & Justin Wolfers, 2010. "Explaining the Favorite-Long Shot Bias: Is it Risk-Love or Misperceptions?," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 723-746, August.
    13. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    14. Nicholas Barberis, 2013. "The Psychology of Tail Events: Progress and Challenges," American Economic Review, American Economic Association, vol. 103(3), pages 611-616, May.
    15. repec:dau:papers:123456789/5461 is not listed on IDEAS
    16. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    17. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    18. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    19. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    20. 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.
    21. Nathalie Etchart-Vincent, 2004. "Is Probability Weighting Sensitive to the Magnitude of Consequences? An Experimental Investigation on Losses," Journal of Risk and Uncertainty, Springer, vol. 28(3), pages 217-235, May.
    22. Lattimore, Pamela K. & Baker, Joanna R. & Witte, Ann D., 1992. "The influence of probability on risky choice: A parametric examination," Journal of Economic Behavior & Organization, Elsevier, vol. 17(3), pages 377-400, May.
    23. Garrett, Thomas A. & Sobel, Russell S., 1999. "Gamblers favor skewness, not risk: Further evidence from United States' lottery games," Economics Letters, Elsevier, vol. 63(1), pages 85-90, April.
    24. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    25. Pamela K. Lattimore & Joanna R. Baker & A. Dryden Witte, 1992. "The Influence Of Probability on Risky Choice: A parametric Examination," NBER Technical Working Papers 0081, National Bureau of Economic Research, Inc.
    26. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
    27. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," The School of Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    28. Quiggin, John, 1991. "On the Optimal Design of Lotteries," Economica, London School of Economics and Political Science, vol. 58(229), pages 1-16, February.
    29. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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    Cited by:

    1. Alexis DIRER, 2010. "Equilibrium Lottery Games and Preferences Under Risk," LEO Working Papers / DR LEO 550, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.

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