Price Interpretability of Prediction Markets: A Convergence Analysis

• 成果类型: Article
• 署名作者: Gao, Jianjun; Wang, Zizhuo; Wu, Weiping; Yu, Dian
• 署名单位: Shanghai University of Finance & Economics; Shanghai University of Finance & Economics; The Chinese University of Hong Kong, Shenzhen; Fuzhou University; Industrial Bank China
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.0417
• 发表日期: 2025
• 关键词: PROSPECT-THEORY; information aggregation; ECONOMICS

摘要

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 marketmaking mechanism for more effective opinion elicitation.