研究企业卖模型给客户如何影响预测效果，揭示市场机制对模型选择的影响。
Markets for Models
- 企业根据数据训练模型并定价，客户可组合多个模型提升预测精度
- 市场结果由模型的偏差-方差分解决定，存在非对称策略选择
- 企业可能故意选低效模型来阻止竞争对手进入，具有策略性动机
鉴于经济中普遍存在预测问题，本文研究企业向消费者出售模型以提升预测能力的市场机制。企业决定是否进入市场，选择在自有数据上训练何种模型，并设定价格。消费者可购买多个模型，通过加权平均组合使用。市场结果可由企业所售模型的偏差-方差分解刻画。我们给出对称企业选择不同建模方法（如仅使用部分协变量）的条件，并表明企业可能主动选择偏差过大或成本过高的模型，以阻止竞争者进入。
原文摘要 · Abstract (English)
Motivated by the prevalence of prediction problems in the economy, we study markets in which firms sell models to a consumer to help improve their prediction. Firms decide whether to enter, choose models to train on their data, and set prices. The consumer can purchase multiple models and use a weighted average of the models bought. Market outcomes can be expressed in terms of the \emph{bias-variance decompositions} of the models that firms sell. We give conditions when symmetric firms will choose different modeling techniques, e.g., each using only a subset of available covariates. We also show firms can choose inefficiently biased models or inefficiently costly models to deter entry by competitors.
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