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Belief Aggregation with Automated Market Makers

Author

Listed:
  • Rajiv Sethi

    (Columbia University)

  • Jennifer Wortman Vaughan

    (Microsoft Research)

Abstract

We consider the properties of a cost function based automated market maker aggregating the beliefs of risk-averse traders with finite budgets. Individuals can interact with the market maker an arbitrary number of times before the state of the world is revealed. We show that the resulting sequence of prices is convergent under general conditions, and explore the properties of the limiting price and trader portfolios. The limiting price cannot be expressed as a function of trader beliefs, since it is sensitive to the market maker’s cost function as well as the order in which traders interact with the market. For a range of trader preferences, however, we show numerically that the limiting price provides a good approximation to a weighted average of beliefs, inclusive of the market designer’s prior belief as reflected in the initial contract price. This average is computed by weighting trader beliefs by their respective budgets, and weighting the initial contract price by the market maker’s worst-case loss, implicit in the cost function. Since cost function parameters are chosen by the market designer, this allows for an inference regarding the budget-weighted average of trader beliefs.

Suggested Citation

  • Rajiv Sethi & Jennifer Wortman Vaughan, 2016. "Belief Aggregation with Automated Market Makers," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 155-178, June.
    • Handle: RePEc:kap:compec:v:48:y:2016:i:1:d:10.1007_s10614-015-9514-7
    DOI: 10.1007/s10614-015-9514-7
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    References listed on IDEAS

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    1. Manski, Charles F., 2006. "Interpreting the predictions of prediction markets," Economics Letters, Elsevier, vol. 91(3), pages 425-429, June.
    2. Berg, Joyce & Forsythe, Robert & Nelson, Forrest & Rietz, Thomas, 2008. "Results from a Dozen Years of Election Futures Markets Research," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 80, pages 742-751, Elsevier.
    3. Andrew Leigh & Justin Wolfers, 2006. "Competing Approaches to Forecasting Elections: Economic Models, Opinion Polling and Prediction Markets," The Economic Record, The Economic Society of Australia, vol. 82(258), pages 325-340, September.
    4. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    5. Krishnamurthy Iyer & Ramesh Johari & Ciamac C. Moallemi, 2014. "Information Aggregation and Allocative Efficiency in Smooth Markets," Management Science, INFORMS, vol. 60(10), pages 2509-2524, October.
    6. Wolfers, Justin & Zitzewitz, Eric, 2006. "Interpreting Prediction Market Prices as Probabilities," IZA Discussion Papers 2092, Institute of Labor Economics (IZA).
    7. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    8. Steven Gjerstad, 2004. "Risk Aversion, Beliefs, and Prediction Market Equilibrium," Microeconomics 0411002, University Library of Munich, Germany.
    9. Michael Ostrovsky, 2012. "Information Aggregation in Dynamic Markets With Strategic Traders," Econometrica, Econometric Society, vol. 80(6), pages 2595-2647, November.
    10. Rothschild, David, 2015. "Combining forecasts for elections: Accurate, relevant, and timely," International Journal of Forecasting, Elsevier, vol. 31(3), pages 952-964.
    11. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
    12. Yiling Chen & Mike Ruberry & Jennifer Wortman Vaughan, 2012. "Designing Informative Securities," Papers 1210.4837, arXiv.org.
    13. 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.
    14. Rajiv Sethi & Muhamet Yildiz, 2012. "Public Disagreement," American Economic Journal: Microeconomics, American Economic Association, vol. 4(3), pages 57-95, August.
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    Cited by:

    1. Dirk Bergemann & Marco Ottaviani, 2021. "Information Markets and Nonmarkets," Cowles Foundation Discussion Papers 2296, Cowles Foundation for Research in Economics, Yale University.
    2. Rajiv Sethi & Julie Seager & Emily Cai & Daniel M. Benjamin & Fred Morstatter, 2021. "Models, Markets, and the Forecasting of Elections," Papers 2102.04936, arXiv.org, revised May 2021.
    3. Christos Alexakis & Michael Dowling & Konstantinos Eleftheriou & Michael Polemis, 2021. "Textual Machine Learning: An Application to Computational Economics Research," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 369-385, January.
    4. Dian Yu & Jianjun Gao & Weiping Wu & Zizhuo Wang, 2022. "Price Interpretability of Prediction Markets: A Convergence Analysis," Papers 2205.08913, arXiv.org, revised Nov 2023.
    5. Majid Karimi & Stanko Dimitrov, 2018. "On the Road to Making Science of “Art”: Risk Bias in Market Scoring Rules," Decision Analysis, INFORMS, vol. 15(2), pages 72-89, June.
    6. Boris Maciejovsky & David V. Budescu, 2020. "Too Much Trust in Group Decisions: Uncovering Hidden Profiles by Groups and Markets," Organization Science, INFORMS, vol. 31(6), pages 1497-1514, November.
    7. Karimi, Majid & Zaerpour, Nima, 2022. "Put your money where your forecast is: Supply chain collaborative forecasting with cost-function-based prediction markets," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1035-1049.

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