The identification of choice models is crucial for understanding consumer behavior and informing marketing or operational strategies, policy design, and product development. The identification of parametric choice-based demand models is typically straightforward. However, nonparametric models, which are highly effective and flexible in explaining customer choice, may encounter the challenge of the dimensionality curse, hindering their identification. A prominent example of a nonparametric model is the ranking-based model, which mirrors the random utility maximization (RUM) class and is known to be nonidentifiable from the collection of choice probabilities alone. Our objective in this paper is to 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. Additionally, our choice model demonstrates competitive prediction accuracy compared to the state-of-the-art benchmarks in a real-world case study, despite incorporating the assumption of bounded rationality which could, in theory, limit the representation power of our model. In addition, we tackle the important problem of finding the optimal assortment under the proposed choice model. We demonstrate the NP-hardness of this problem and provide a fully polynomial-time approximation scheme through dynamic programming. Additionally, we propose an efficient estimation framework using a combination of column generation and expectation-maximization algorithms, which proves to be more tractable than the estimation algorithm of the aforementioned ranking-based model.

翻译：选择模型的识别对于理解消费者行为以及指导营销或运营策略、政策制定和产品开发至关重要。基于参数化选择的需求模型的识别通常较为直接。然而，非参数模型在解释顾客选择方面虽然高效且灵活，但可能面临维数灾难的挑战，从而阻碍其识别。一个典型的非参数模型是基于排名的模型，它反映了随机效用最大化（RUM）类别，并且已知仅从选择概率的集合中无法识别。本文的目标是开发一类新的非参数模型，该模型不受不可识别性问题的困扰。我们的模型假设消费者具有有限理性，这导致了对称的需求蚕食现象，并有趣地实现了完全识别。此外，尽管我们的选择模型纳入了可能在理论上限制其表达能力的有限理性假设，但在实际案例研究中，其预测精度与最先进的基准模型相比仍具有竞争力。我们还针对所提出的选择模型解决了最优商品组合排序这一重要问题。我们证明了该问题的NP难度，并通过动态规划提供了一个完全多项式时间近似方案。此外，我们提出了一种结合列生成和期望最大化算法的高效估计框架，该框架比前述基于排名模型的估计算法更具可解性。