Learning Valuation Distributions from Bundle Sales

Abstract

Bundling has long been used as a form of price discrimination, allowing for items to be sold at a discount when they are purchased together with others. In this paper, we show that bundling has the added benefit of leading to richer sales data, providing more information about customer demand than individual sales.

We introduce the problem of reconstructing the valuation distributions which would fit a set of bundle sales numbers. We show that a fundamental class of customer valuation models (unit-demand, additive, independent) can be identified from such data, and solve the corresponding fitting problem by deriving an iterative algorithm and establishing convergence. An important insight from fitting this simple class of models is that an item's price elasticity can be measured by comparing its sales rates inside and outside of bundles.

Finally, we validate this insight on data from a large online retailer, where indeed, the price elasticities of items, as indicated by their sales spikes after a Black Friday markdown, are consistent with their bundle sales before Black Friday.

Keywords: bundling, valuation learning, revenue management