A Generalized Markov Chain Model to Capture Dynamic Preferences and Choice Overload

TL;DR

This paper introduces a generalized Markov chain choice model that captures dynamic preferences and choice overload, addressing limitations of traditional models by allowing purchase probabilities to decrease with larger assortments.

Contribution

It extends existing Markov chain choice models to incorporate choice overload effects and provides an FPTAS for assortment optimization under this new model.

Findings

Model captures decreasing purchase probabilities with larger assortments.

Assortment optimization is NP-hard but admits an FPTAS.

Generalizes MNL with assortment-dependent no-purchase attractions.

Abstract

Assortment optimization is an important problem that arises in many industries such as retailing and online advertising where the goal is to find a subset of products from a universe of substitutable products which maximize seller's expected revenue. One of the key challenges in this problem is to model the customer substitution behavior. Many parametric random utility maximization (RUM) based choice models have been considered in the literature. However, in all these models, probability of purchase increases as we include more products to an assortment. This is not true in general and in many settings more choices hurt sales. This is commonly referred to as the choice overload. In this paper we attempt to address this limitation in RUM through a generalization of the Markov chain based choice model considered in Blanchet et al. (2016). As a special case, we show that our model reduces to a generalization of MNL with no-purchase attractions dependent on the assortment S and strictly increasing with the size of assortment S. While we show that the assortment optimization under this model is NP-hard, we present fully polynomial-time approximation scheme (FPTAS) under reasonable assumptions.