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Far from the Madding Crowd: Collective Wisdom in Prediction Markets

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  • Giulio Bottazzi
  • Daniele Giachini

Abstract

We investigate market selection and bet pricing in a simple Arrow security economy which we show is equivalent to the repeated prediction mar- ket models studied in the literature. We derive the condition for long run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of two fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities. Nor are they always nearer to the truth than the believes of all surviving agents. Moreover, we show that by adapting their beliefs to past prices, agents further decrease the agreement between market prices and true probabilities.

Suggested Citation

  • Giulio Bottazzi & Daniele Giachini, 2016. "Far from the Madding Crowd: Collective Wisdom in Prediction Markets," LEM Papers Series 2016/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2016/14
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Dindo, Pietro & Massari, Filippo, 2020. "The wisdom of the crowd in dynamic economies," Theoretical Economics, Econometric Society, vol. 15(4), November.
    2. Tang, Ming & Liao, Huchang, 2024. "Group efficiency and individual fairness tradeoff in making wise decisions," Omega, Elsevier, vol. 124(C).
    3. Bottazzi, Giulio & Giachini, Daniele & Ottaviani, Matteo, 2023. "Market selection and learning under model misspecification," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    4. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    5. Fontanelli, Luca & Guerini, Mattia & Napoletano, Mauro, 2023. "International trade and technological competition in markets with dynamic increasing returns," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    6. Vandin, Andrea & Giachini, Daniele & Lamperti, Francesco & Chiaromonte, Francesca, 2022. "Automated and distributed statistical analysis of economic agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    7. Mikhail Zhitlukhin, 2021. "Asymptotically optimal strategies in a diffusion approximation of a repeated betting game," Papers 2108.11998, arXiv.org.
    8. Daniele Giachini, 2018. "Rationality and Asset Prices under Belief Heterogeneity," LEM Papers Series 2018/07, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    9. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2020. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," LEM Papers Series 2020/31, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    10. Bottazzi, Giulio & Giachini, Daniele, 2017. "Wealth and price distribution by diffusive approximation in a repeated prediction market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 473-479.
    11. Nina Badulina & Dmitry Shatilovich & Mikhail Zhitlukhin, 2024. "On convergence of forecasts in prediction markets," Papers 2402.16345, arXiv.org.
    12. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    13. Fabio Della Rossa & Lorenzo Giannini & Pietro DeLellis, 2020. "Herding or wisdom of the crowd? Controlling efficiency in a partially rational financial market," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-16, September.
    14. Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    15. Bottazzi, Giulio & Dindo, Pietro, 2022. "Drift criteria for persistence of discrete stochastic processes on the line," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    16. Giulio Bottazzi & Daniele Giachini, 2018. "New Results on Betting Strategies, Market Selection, and the Role of Luck," LEM Papers Series 2018/08, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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