Adaptive Pricing for Customers with Probabilistic Valuations

In this paper, we examine the problem of choosing discriminatory prices for customers with probabilistic valuations and a seller with indistinguishable copies of a good. We show that under certain assumptions this problem can be reduced to the continuous knapsack problem (CKP). We present a new fast ǫ-optimal algorithm for solving CKP instances with asymmetric concave reward functions. We also show that our algorithm can be extended beyond the CKP setting to handle pricing problems with overlapping goods (e.g.goods with common components or common resource requirements), rather than indistinguishable goods. We provide a framework for learning distributions over customer valuations from historical data that are accurate and compatible with our CKP algorithm, and we validate our techniques with experiments on pricing instances derived from the Trading Agent Competition in Supply Chain Management (TAC SCM). Our results confirm that our algorithm converges to an ǫ-optimal solution more quickly in practice than an adaptation of a previously proposed greedy heuristic.