Model-Free Assortment Pricing with Transaction Data

We study the problem when a firm sets prices for products based on the transaction data, that is, which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The uncertainty set of potential valuations of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst case revenue, assuming that new customers’ valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We study the single-product case analytically and relate it to the traditional model-based approach. Then, we show that the optimal prices in the general case can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. We further design three approximation strategies that are of low computational complexity and interpretable. In particular, the cutoff pricing heuristic has a competent provable performance guarantee. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.