Learning to Price Supply Chain Contracts Against a Learning Retailer.

This article addresses the supply chain contract design problem faced by a data-driven supplier who must set wholesale prices in response to a downstream retailer employing unknown, dynamic inventory learning policies under uncertain and potentially nonstationary market demand. The supplier’s goal is to develop pricing policies that achieve sublinear regret compared to a clairvoyant with full knowledge of the retailer’s ordering decisions, despite not observing demand realizations or the retailer’s learning policy. To capture the retailer-induced nonstationarity, the authors introduce a novel variation budget based on the Kolmogorov distance between the retailer’s estimated demand distributions, which better quantifies environmental changes than existing models. They propose two dynamic pricing algorithms—LUNA for discrete demand distributions and LUNAC for continuous demand distributions—that adapt to a wide range of retailer policies and achieve sublinear regret bounds without requiring knowledge of the retailer’s policy or demand support. Numerical experiments demonstrate that these algorithms outperform standard nonstationary bandit benchmarks, highlighting the value of exploiting structural properties in data-driven supply chain management. Extensions include handling dynamic retailer selling prices and prohibiting supplier pricing below cost, with corresponding regret analyses provided.