预测市场中预测误差的分解
A Decomposition of Forecast Error in Prediction Markets
摘要：
我们分析预测市场预测的误差来源，以限制证券价格与其估计的真实价格之间的差异。我们考虑基于成本函数的预测市场，其中自动做市商根据交易历史调整证券价格。我们将预测误差分解为三个部分：抽样误差，因为交易者只拥有对地面真相的嘈杂估计而产生;做市商偏见，由于使用特定的做市商（即，成本函数），以促进贸易;和收敛误差，产生的，因为在任何时候，市场价格可能仍然在不断变化。我们的目标是明确这些误差分量之间的权衡，受设计决策的影响，如成本函数的函数形式和市场的流动性。我们考虑一个特定的模型，在该模型中，交易者具有指数效用和指数家族信念，代表对地面真实的噪声估计。在这种情况下，抽样误差随着交易者数量的增加而消失，但其他两个组成部分之间存在权衡。我们提供了做市商偏差和收敛误差的上界和下界，并通过数值模拟证明这些界是紧的。我们的研究结果产生了新的见解，如何设置市场的流动性参数的问题，并到执行一致的价格在证券的预测效益。
英文摘要：
We analyze sources of error in prediction market forecasts in order to bound the difference between a security's price and the ground truth it estimates. We consider cost-function-based prediction markets in which an automated market maker adjusts security prices according to the history of trade. We decompose the forecasting error into three components: sampling error, arising because traders only possess noisy estimates of ground truth; market-maker bias, resulting from the use of a particular market maker (i.e., cost function) to facilitate trade; and convergence error, arising because, at any point in time, market prices may still be in flux. Our goal is to make explicit the tradeoffs between these error components, influenced by design decisions such as the functional form of the cost function and the amount of liquidity in the market. We consider a specific model in which traders have exponential utility and exponential-family beliefs representing noisy estimates of ground truth. In this setting, sampling error vanishes as the number of traders grows, but there is a tradeoff between the other two components. We provide both upper and lower bounds on market-maker bias and convergence error, and demonstrate via numerical simulations that these bounds are tight. Our results yield new insights into the question of how to set the market's liquidity parameter and into the forecasting benefits of enforcing coherent prices across securities.
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