Two-Sided Pricing and Learning with Buyer Choice: A Generalized SGD Method

Motivated by online used-car platforms, we study pricing decisions for purchasing and selling multiple products in a two-sided market. Whereas supply for each product is independently acquired from individual sellers, demand is substitutable and follows a choice model. With uncertainty from both supply and demand, a platform sequentially adjusts purchase and selling prices to maximize profit while satisfying inventory constraints. Moreover, the platform does not know in advance the supply and demand as functions of prices. The pricing decisions should account for learning of the supply and demand functions in addition to the two sides of uncertainty and potential stockouts. When the supply and demand functions are known, we find a class of fixed-price policies that achieve provably good performance. Our finding suggests that we can target a fixed-price policy rather than the state-dependent optimal policy when the supply and demand functions are unknown. We propose a novel generalization of the classical stochastic gradient descent (SGD) method for learning the target prices on each side. Our algorithm with the generalized SGD is asymptotically optimal when the planning horizon is large.

Funding: M. Lin acknowledges that the study was funded in the Singapore Management University through the research [Grant 22-LKCSB-SMU-097] from the Ministry of Education Academic Research Fund Tier 1. W. T. Huh acknowledges support from the Natural Sciences and Engineering Research Council of Canada through Discovery [Grant RGPIN-2020-04213], as well as from the Canada Research Chairs Program.

Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2025.1786.