The identification of choice models is crucial for understanding consumer behavior, designing marketing policies, and developing new products. The identification of parametric choice-based demand models, such as the multinomial choice model (MNL), is typically straightforward. However, nonparametric models, which are highly effective and flexible in explaining customer choices, may encounter the curse of the dimensionality and lose their identifiability. For example, the ranking-based model, which is a nonparametric model and designed to mirror the random utility maximization (RUM) principle, is known to be nonidentifiable from the collection of choice probabilities alone. In this paper, we develop a new class of nonparametric models that is not subject to the problem of nonidentifiability. Our model assumes bounded rationality of consumers, which results in symmetric demand cannibalization and intriguingly enables full identification. That is to say, we can uniquely construct the model based on its observed choice probabilities over assortments. We further propose an efficient estimation framework using a combination of column generation and expectation-maximization algorithms. Using a real-world data, we show that our choice model demonstrates competitive prediction accuracy compared to the state-of-the-art benchmarks, despite incorporating the assumption of bounded rationality which could, in theory, limit the representation power of our model.

翻译：选择模型的辨识对于理解消费者行为、设计营销策略以及开发新产品至关重要。传统参数化选择需求模型（如多项式选择模型MNL）的辨识通常较为直接。然而，非参数模型虽在解释消费者选择方面高度有效且灵活，却可能遭遇维度灾难并丧失可辨识性。例如，基于排名的模型作为非参数模型，旨在反映随机效用最大化（RUM）原则，但仅凭选择概率集合已知无法辨识。本文提出了一类不受非可辨识性困扰的新型非参数模型。该模型假设消费者具有有限理性，由此产生对称的需求蚕食现象，并有趣地实现了完全辨识——即我们可以基于在备选集合上观测到的选择概率唯一地重构该模型。我们进一步提出了结合列生成与期望最大化算法的高效估计框架。基于真实数据的实验表明，尽管我们的模型引入了有限理性假设（理论上可能限制模型表征能力），但其预测精度与最先进的基准模型相比仍具竞争力。