  We study the problem when a firm sets prices for products based on the
transaction data, i.e., 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 individual valuation 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 show that the optimal prices in
this setting can be approximated at any arbitrary precision by solving a
compact mixed-integer linear program. Moreover, we study the single-product
case and relate it to the traditional model-based approach. We also design
three approximation strategies that are of low computational complexity and
interpretable. 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.
