A Nonparametric Stochastic Set Model: Identification, Optimization, and Prediction

51 Pages Posted: 10 Feb 2023 Last revised: 17 Jul 2023

See all articles by Yi-Chun Akchen

Yi-Chun Akchen

University College London - School of Management

Dmitry Mitrofanov

Boston College, Carroll School of Management

Date Written: February 8, 2023

Abstract

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.

Keywords: bounded rationality, consideration set, symmetric cannibalization, assortment optimization, FPTAS, case study

Suggested Citation

Akchen, Yi-Chun and Mitrofanov, Dmitry, A Nonparametric Stochastic Set Model: Identification, Optimization, and Prediction (February 8, 2023). Available at SSRN: https://ssrn.com/abstract=4352043 or http://dx.doi.org/10.2139/ssrn.4352043

Yi-Chun Akchen (Contact Author)

University College London - School of Management ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Dmitry Mitrofanov

Boston College, Carroll School of Management

257 Beacon Street
Chestnut Hill, MA 02467
United States

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