Price Interpretability of Prediction Markets: A Convergence Analysis

Jianjun Gao (), Zizhuo Wang (), Weiping Wu () and Dian Yu ()
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Jianjun Gao: School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China; and Key Laboratory of Interdisciplinary Research of Computation and Economics, Shanghai University of Finance and Economics, Ministry of Education, Shanghai 200433, China
Zizhuo Wang: School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China
Weiping Wu: School of Economics and Management, Fuzhou University, Fuzhou 350108, China
Dian Yu: Industrial Bank, Co., Ltd., Fuzhou 350014, China

Operations Research, 2025, vol. 73, issue 1, 157-177

Abstract: Prediction markets are long known for prediction accuracy. This study systematically explores the fundamental properties of prediction markets, addressing questions about their information aggregation process and the factors contributing to their remarkable efficacy. We propose a novel multivariate utility–based mechanism that unifies several existing automated market-making schemes. Using this mechanism, we establish the convergence results for markets comprised of risk-averse traders who have heterogeneous beliefs and repeatedly interact with the market maker. We demonstrate that the resulting limiting wealth distribution aligns with the Pareto efficient frontier defined by the utilities of all market participants. With the help of this result, we establish analytical and numerical results for the limiting price in different market models. Specifically, we show that the limiting price converges to the geometric mean of agent beliefs in exponential utility-based markets. In risk measure-based markets, we construct a family of risk measures that satisfy the convergence criteria and prove that the price converges to a unique level represented by the weighted power mean of agent beliefs. In broader markets with constant relative risk aversion utilities, we reveal that the limiting price can be characterized by systems of equations that encapsulate agent beliefs, risk parameters, and wealth. Despite the impact of traders’ trading sequences on the limiting price, we establish a price invariance result for markets with a large trader population. Using this result, we propose an efficient approximation scheme for the limiting price. Numerical experiments demonstrate that the accuracy of this approximation scheme outperforms existing approximation methods across various scenarios. Our findings serve to aid market designers in better tailoring and adjusting the market-making mechanism for more effective opinion elicitation.

Keywords: Market Analytics and Revenue Management; dynamic mechanisms; information elicitation; prediction markets (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:1:p:157-177

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