Learning Consumer Preferences from Bundle Sales Data

TL;DR

This paper introduces a novel method to estimate consumer valuation distributions from bundle sales data, addressing the limitations of classical choice models in multi-product purchase scenarios.

Contribution

It develops an EM-based estimation framework that handles censored data, unobserved no-purchases, and market segmentation, with theoretical guarantees.

Findings

Successfully recovers consumer valuation distributions from simulated data.

Provides theoretical results on model identifiability and EM convergence.

Demonstrates effectiveness through numerical experiments.

Abstract

Product bundling is a common selling mechanism used in online retailing. To set profitable bundle prices, the seller needs to learn consumer preferences from the transaction data. When customers purchase bundles or multiple products, classical methods such as discrete choice models cannot be used to estimate customers' valuations. In this paper, we propose an approach to learn the distribution of consumers' valuations toward the products using bundle sales data. The approach reduces it to an estimation problem where the samples are censored by polyhedral regions. Using the EM algorithm and Monte Carlo simulation, our approach can recover the distribution of consumers' valuations. The framework allows for unobserved no-purchases and clustered market segments. We provide theoretical results on the identifiability of the probability model and the convergence of the EM algorithm. The performance of the approach is also demonstrated numerically.