Two-Sided Pricing and Learning with Inventory Constraints
32 Pages Posted: 14 Mar 2024
Date Written: February 15, 2024
Abstract
Motivated by online used-car platforms, we study pricing decisions for purchasing and selling a product in a two-sided market. 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 how supply and demand depend on the prices. The pricing decisions should account for learning of the supply and demand functions in addition to the two sides of uncertainty and inventory constraints. We study first pricing for the demand side with uncertain supply and then the two-sided pricing problem. For each problem, we start with the clairvoyant’s problem with known supply and demand functions. We show that a fixed-price policy is asymptotically optimal and establish a bound on its performance loss from the optimal policy. Our bound suggests that we can target the fixed-price policy rather than the state-dependent optimal policy when the supply and demand functions are unknown. By exploiting properties of the fixed-price policy, we propose a pricing algorithm that learns the optimal fixed price(s) and achieves the best possible performance when the planning horizon is large. Our work provides insights into how the platform can manage demand and supply in the presence of the two sides of uncertainty. When the demand and supply functions are known, a simple fixed-price policy can be implemented with a small performance loss. Given limited information on supply and demand, our pricing algorithm is easy to implement and sheds light on how to balance the trade-off between two sides of learning and profit maximization (earning).
Keywords: pricing for demand and supply, online learning, exploration-exploitation trade-off, regret analysis
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