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 (MU) 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 can converge to a unique level represented by the weighted power mean of agent beliefs. In broader markets with Constant Relative Risk Aversion (CRRA) utilities, we reveal that the limiting price can be characterized by systems of equations that encapsulate agent beliefs, risk parameters, and wealth. Despite the potential 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.

翻译：预测市场长期以来以其预测准确性而闻名。本研究系统性地探索了预测市场的基本特性，探讨了其信息聚合过程以及促成其卓越效能的因素。我们提出了一种新颖的基于多元效用（MU）的机制，该机制统一了若干现有的自动化做市方案。借助这一机制，我们为包含具有异质性信念且与做市商反复互动的风险规避交易者的市场建立了收敛性结果。我们证明，由此产生的极限财富分布与所有市场参与者效用所定义的帕累托有效前沿一致。在此结果帮助下，我们针对不同市场模型中的极限价格建立了分析性和数值性结果。具体而言，我们表明，在指数效用市场中，极限价格收敛于交易者信念的几何平均值。在基于风险度量的市场中，我们构建了一族满足收敛条件的风险度量，并证明价格可收敛至由交易者信念的加权幂平均所表示的唯一定值。在具有常相对风险厌恶（CRRA）效用的更广泛市场中，我们揭示极限价格可由包含交易者信念、风险参数与财富的方程组来刻画。尽管交易者的交易序列可能对极限价格产生影响，但对于人口规模较大的市场，我们建立了一个价格不变性结果。利用该结果，我们提出了一种高效的极限价格近似方案。