发表机构
University of Chicago; Kalshi Research; New York University, Shanghai（芝加哥大学; 卡尔希研究公司; 纽约大学上海分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究预测市场中预言家获利问题，通过建立预测准确性与盈利能力的等价关系，给出依赖预测和市场价格的适当投注策略，实证表明此策略能将准确性转化为利润，在Kalshi实时部署获高回报率。
AI 中文摘要
预测市场将分散的信念汇总为价格，作为不确定事件的概率预测。经典理论在特定自动化做市商（AMM）设计下建立了预测准确性与交易利润的清晰等价关系。但如今最大的交易所以限价订单簿为基础，有信息的预测者常亏损，无信息的策略靠简单启发式可获利。我们通过建立预测准确性与盈利能力的形式等价关系解决了这一差异。对于任何严格适当的评分规则\(S\)，展示了一种“适当”的投注策略，仅取决于预测者的预测\(\mathbf{p}\)和市场价格\(\mathbf{q}\)，在\(S\)下\(\mathbf{p}\)优于\(\mathbf{q}\)且市场有足够流动性时能获得正预期利润。此外，这种适当投注本质上是唯一有如此稳健盈利保证的策略。证明基于预期利润的分解，严格推广了经典AMM保证，并解释了无准确性优势时策略如何获利。实证上，在AI模型的数千次预测中，适当投注是唯一能可靠将准确性转化为利润的策略，还识别了系统预测角色并展示了最优适当策略如何因之而异。在Kalshi进行的为期一个月的实时部署实现了\(+80.33\%\)的投资回报率，夏普比率为\(3.35\)。
英文摘要
Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes how a better-than-market forecast can yield positive trading profit. However, it hinges crucially on the specific automated market maker (AMM) design, and is not applicable to popular exchanges today which are based on central limit order books. This paper fills that gap. For any prediction market and any proper scoring rule $S$, we exhibit a ``proper'' betting strategy that depends only on the forecaster's prediction $\mathbf{p}$ and the market price $\mathbf{q}$, and earns positive expected profit \emph{whenever} $\mathbf{p}$ outperforms $\mathbf{q}$ under $S$ and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. Our proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit even without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. For feasibility demonstration, we run a monthlong live pilot test on Kalshi; the encouraging preliminary results show that proper betting can survive real-world spreads, fees, discrete fills, and limited liquidity.
