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An axiomatic characterization of wagering mechanisms

Author

Listed:
  • Lambert, Nicolas S.
  • Langford, John
  • Wortman Vaughan, Jennifer
  • Chen, Yiling
  • Reeves, Daniel M.
  • Shoham, Yoav
  • Pennock, David M.

Abstract

We construct a budget-balanced wagering mechanism that flexibly extracts information about event probabilities, as well as the mean, median, and other statistics from a group of individuals whose beliefs are immutable to the actions of others. We show how our mechanism, called the Brier betting mechanism, arises naturally from a modified parimutuel betting market. We prove that it is essentially the unique wagering mechanism that is anonymous, proportional, sybilproof, and homogeneous. While the Brier betting mechanism is designed for individuals with immutable beliefs, we find that it continues to perform well even for Bayesian individuals who learn from the actions of others.

Suggested Citation

  • Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
    • Handle: RePEc:eee:jetheo:v:156:y:2015:i:c:p:389-416
    DOI: 10.1016/j.jet.2014.03.012
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    as
    1. Richard E. Quandt, 1986. "Betting and Equilibrium," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(1), pages 201-207.
    2. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    3. Osband, Kent, 1989. "Optimal Forecasting Incentives," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1091-1112, October.
    4. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    5. Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," Journal of Economic Perspectives, American Economic Association, vol. 18(2), pages 107-126, Spring.
    6. Charles R. Plott & Jorgen Wit & Winston C. Yang, 2003. "Parimutuel betting markets as information aggregation devices: experimental results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 311-351, September.
    7. Plott, Charles R & Sunder, Shyam, 1982. "Efficiency of Experimental Security Markets with Insider Information: An Application of Rational-Expectations Models," Journal of Political Economy, University of Chicago Press, vol. 90(4), pages 663-698, August.
    8. Robert T. Clemen & Robert L. Winkler, 1999. "Combining Probability Distributions From Experts in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 19(2), pages 187-203, April.
    9. Sanford J. Grossman, 1981. "An Introduction to the Theory of Rational Expectations Under Asymmetric Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 541-559.
    10. Forsythe, Robert & Lundholm, Russell, 1990. "Information Aggregation in an Experimental Market," Econometrica, Econometric Society, vol. 58(2), pages 309-347, March.
    11. R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 1-60, June.
    12. Hurley, William & McDonough, Lawrence, 1995. "A Note on the Hayek Hypothesis and the Favorite-Longshot Bias in Parimutuel Betting," American Economic Review, American Economic Association, vol. 85(4), pages 949-955, September.
    13. Michael Ostrovsky, 2012. "Information Aggregation in Dynamic Markets With Strategic Traders," Econometrica, Econometric Society, vol. 80(6), pages 2595-2647, November.
    14. Robert F. Nau, 1985. "Should Scoring Rules be "Effective"?," Management Science, INFORMS, vol. 31(5), pages 527-535, May.
    15. Marco Ottaviani & Peter Norman Sorensen, 2010. "Noise, Information, and the Favorite-Longshot Bias in Parimutuel Predictions," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 58-85, February.
    16. Thaler, Richard H & Ziemba, William T, 1988. "Parimutuel Betting Markets: Racetracks and Lotteries," Journal of Economic Perspectives, American Economic Association, vol. 2(2), pages 161-174, Spring.
    17. Plott, Charles R & Sunder, Shyam, 1988. "Rational Expectations and the Aggregation of Diverse Information in Laboratory Security Markets," Econometrica, Econometric Society, vol. 56(5), pages 1085-1118, September.
    18. Daniel Friedman, 1983. "Effective Scoring Rules for Probabilistic Forecasts," Management Science, INFORMS, vol. 29(4), pages 447-454, April.
    19. Watanabe, Takahiro & Nonoyama, Hideyuki & Mori, Masao, 1994. "A Model of a General Parimutuel System: Characterizations and Equilibrium Selection," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 237-260.
    20. Koessler, Frédéric & Noussair, Charles & Ziegelmeyer, Anthony, 2008. "Parimutuel betting under asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 733-744, July.
    21. David J. Johnstone, 2007. "The Parimutuel Kelly Probability Scoring Rule," Decision Analysis, INFORMS, vol. 4(2), pages 66-75, June.
    22. Marco Ottaviani & Peter Norman Sørensen, 2009. "Surprised by the Parimutuel Odds?," American Economic Review, American Economic Association, vol. 99(5), pages 2129-2134, December.
    23. Takahiro, Watanabe, 1997. "A parimutuel system with two horses and a continuum of bettors," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 85-100, August.
    24. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
    25. Emir Shuford & Arthur Albert & H. Edward Massengill, 1966. "Admissible probability measurement procedures," Psychometrika, Springer;The Psychometric Society, vol. 31(2), pages 125-145, June.
    26. Forsythe, Robert & Forrest Nelson & George R. Neumann & Jack Wright, 1992. "Anatomy of an Experimental Political Stock Market," American Economic Review, American Economic Association, vol. 82(5), pages 1142-1161, December.
    27. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    28. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    29. Ali, Mukhtar M, 1977. "Probability and Utility Estimates for Racetrack Bettors," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 803-815, August.
    30. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2009. "Sensitivity to Distance and Baseline Distributions in Forecast Evaluation," Management Science, INFORMS, vol. 55(4), pages 582-590, April.
    31. D. Marc Kilgour & Yigal Gerchak, 2004. "Elicitation of Probabilities Using Competitive Scoring Rules," Decision Analysis, INFORMS, vol. 1(2), pages 108-113, June.
    32. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    33. Scott E. Page, 2007. "Prologue to The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies," Introductory Chapters, in: The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies, Princeton University Press.
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    5. Robert L. Winkler & Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose, 2019. "Probability Forecasts and Their Combination: A Research Perspective," Decision Analysis, INFORMS, vol. 16(4), pages 239-260, December.

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    More about this item

    Keywords

    Betting market; Wagering mechanism; Parimutuel betting; Scoring rule; Belief elicitation; Prediction market;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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