Learning-Based Bundling Strategy for Two Products Under Uncertain Consumer's Valuations

Should a firm engage in bundling to boost revenue when consumer's valuations of products are heterogeneous and uncertain? In recent years, technological advances have made it possible for firms to use large amounts of available data to make decisions under demand-side information uncertainty. However, it remains unclear exactly how they can dynamically optimize bundling and pricing decisions by learning from uncertain consumer's valuations. To answer this question, we study the bundling and pricing decisions of a monopoly firm offering a basic product and a premium product over a finite T periods. We first analyze the equilibrium outcomes of pure component strategies (PCS) and pure bundling strategies (PBS) under deterministic consumer's valuations. We then introduce a learning-based bundling strategy (LBBS) framework to make decisions dynamically over time. It employs Thompson Sampling to estimate the fractions of low-valuation consumers (LVC) of two products, allowing the firm to adjust its decisions based on updated beliefs about consumer's valuation distributions. We demonstrate the robust performance of the LBBS and show the interesting findings. That is, the fraction of LVC of premium product, the ratio between high- and low-valuation (RHL) of basic product, the ratio of low-valuation (RLV) and the ratio of high-valuation (RHV) of two products wield significant influence on the adoption of bundling strategy and its possibility. These findings offer practical guidance to firm's practitioners regarding when and which PBS to adopt and how to improve PBS decisions according to the fractions of LVC of products. We also extend the model to uniform distribution of consumer's valuations and correlated consumer's valuations to test our results.