Journal of Risk and Uncertainty

, Volume 22, Issue 3, pp 251–261 | Cite as

The Medium Prizes Paradox: Evidence From a Simulated Casino

  • Ernan Haruvy
  • Ido Erev
  • Doron Sonsino
Article

Abstract

Mainstream explanations to gambling specify conditions under which human agents are locally risk loving. Such theories, however, fail to explain the typically observed prize distribution of a few large prizes and a large number of medium ones—hence the medium prizes paradox. In the current study we show that adaptive learning models recently proposed in the literature offer a solution. Simulations of such models predict that multiple medium prizes will slow down the decrease (over time) in agents' inclination to gamble. We run a laboratory experiment that supports this explanation and shows that the positive effect of medium prizes on the inclination to gamble increases with time.

gambling reinforcement learning 

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References

  1. Bereby-Meyer, Y. and I. Erev. (1998). “On Learning To Become a Successful Loser: A Comparison of Alternative Abstractions of Learning Processes in the Loss Domain,” Journal of Mathematical Psychology 42, 266–286.Google Scholar
  2. Borgers, T. and R. Sarin. (1997). “Naive reinforcement learning with endogenous aspirations,” mimeo. University College London and Texas A&M University.Google Scholar
  3. Brandts, J. and C. Holt. (1996). “Naive Bayesian Learning and Adjustment to Equilibrium in Signaling Games,” working paper, University of Virginia.Google Scholar
  4. Bush, R. R. and Mosteller, F. (1955). Stochastic Models for Learning, Wiley, New York.Google Scholar
  5. Camerer, C. and T. Ho. (1999). “Experience Weighted Attraction Learning in Normal Form Games,” Econometrica 67, 827–874.Google Scholar
  6. Carbone, E. and J. D. Hey. (1994). “Discriminating Between Preference Functionals—A Preliminary Monte Carlo Study,” Journal of Risk and Uncertainty 8, 223–242.Google Scholar
  7. Carbone, E. and J. D. Hey. (2000). “Which Error Story is Best?,” Journal of Risk and Uncertainty 20, 161–176.Google Scholar
  8. Cheung, Y. and D. Friedman. (1997). “Individual Learning in Normal Form Games: Some Laboratory Results,” Games and Economic Behavior 19, 46–76.Google Scholar
  9. Christiansen, E. M. (1998). “Gambling and the American Economy,” Annals of the American Academy of Political and Social Science 556, 36–52.Google Scholar
  10. Clotfelter, C. T. and P. J. Cook. (1989). “The Demand for Lottery Products,” National Bureau of Economic Research Working Paper 2928.Google Scholar
  11. Crawford, V. (1995). “Adaptive Dynamics in Coordination Games,” Econometrica 63, 103–144.Google Scholar
  12. Devereux, E. C. (1968). “Gambling.” In David L. Sills (ed.), International Encyclopedia of the Social Sciences. New York: The Macmillan Company and the Free Press.Google Scholar
  13. Erev, I., Y. Bereby-Meyer, and A. Roth. (1999). “The Effect of Adding a Constant to All Payoffs: Experimental Investigation, and Implications for Reinforcement Learning Models,” Journal of Economic Behavior and Organization 39, 111–128.Google Scholar
  14. Erev, I. and A. Roth. (1998). “Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique Mixed Strategy Equilibria,” American Economic Review 88, 848–881.Google Scholar
  15. Friedman, M. and L. J. Savage. (1948). “The Utility Analysis of Choice Involving Risk,” Journal of Political Economy 56, 279–304.Google Scholar
  16. Fudenberg, D. and D. K. Levine. (1998). The Theory of Learning in Games. Cambridge, MA: MIT Press.Google Scholar
  17. Machina, M. (1982). “Expected Utility Analysis Without the Independence Axiom,” Econometrica 50, 277–323.Google Scholar
  18. Ng, Y. K. (1975). “Why Do People Buy Lottery Tickets? Choice Involving Risk and the Indivisibility of Expenditure,” Journal of Political Economy 73, 530–535.Google Scholar
  19. Quiggin, J. (1991). “On the Optimal Design of Lotteries,” Economica 58, 1–16.Google Scholar
  20. Robson, A. (1996). “The Evolution of Attitudes to Risk: Lottery Tickets and Relative Wealth,” Games and Economic Behavior 14, 190–207.Google Scholar
  21. Roth, A. and I. Erev. (1995). “Learning in Extensive Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term,” Games and Economic Behavior 8, 164–212.Google Scholar
  22. Sadler, M. (2000). “Escaping Poverty: Risk-Taking and Endogenous Inequality in a Model of Equilibrium Growth,” Review of Economic Dynamics, 3, 704–725.Google Scholar
  23. Sarin, R. and F. Vahid. (2001). “Predicting How People Play Games: A Simple Dynamic Model of Choice,” Games and Economic Behavior, 34, 104–122.Google Scholar
  24. Skinner, B. F. (1953). Science and Human Behavior. New York: The Free Press.Google Scholar
  25. Stahl, D. (1996). “Boundedly Rational Rule Learning in a Guessing Game,” Games and Economic Behavior 16, 303–330.Google Scholar
  26. Tang, F.-F. (1996). “Anticipatory Learning in Two-Person Games: An Experimental Study,” Discussion paper B-363, University of Bonn.Google Scholar
  27. Tversky, A. and D. Kahneman. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, 297–323.Google Scholar
  28. Van Huyck, J., J. Cook, and R. Battalio. (1997). “Adaptive Behavior and Coordination Failure,” Journal of Economic Behavior and Organization 32, 483–503.Google Scholar
  29. Viscusi, W. K. (1989). “Prospective Reference Theory: Towards and Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–263.Google Scholar
  30. Wakker, P., I. Erev, and E. Weber. (1994). “Comonotonic Independence: The Critical Test Between Classical and Rank-Dependent Utility Theories,” Journal of Risk and Uncertainty 9, 195–230.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Ernan Haruvy
    • 1
  • Ido Erev
    • 1
  • Doron Sonsino
    • 1
  1. 1.Faculty of Industrial Engineering and ManagementTechnion, HaifaIsrael

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