Learning Valuation Distributions from Bundle Prices

Abstract

Bundling has been widely studied in the literature as a form of price discrimination. We show that it can also be used as a form of price experimentation: sales data from bundling schemes contains richer information about the latent customer valuations than individual sales data, allowing the firm to learn both the mean valuations and the price elasticities without changing any prices. We develop an iterative algorithm that can reconstruct independent valuation distributions from noisy observations under Mixed Bundling, and converges with high probability. Furthermore, we show that Mixed Bundling and two-part tariffs are complementary pricing schemes from a learning point of view, so our algorithm can also learn from two-part tariffs, which are profitable pricing schemes in their own right. We verify the efficacy of our methodology in numerical experiments, demonstrating that with a realistic number of data points, optimizing over the inferred distributions extracts nearly all of the optimal profit obtainable had we known the true distributions.