Dynamic Wholesale Pricing under Censored-Demand Learning

Abstract

This paper studies dynamic wholesale pricing and ordering in a two-tier supply chain where firms share POS data and learn about demand from censored demand data. When stockouts occur, unmet demand is unobserved, so the retailer's order quantity affects not only current profits but also the informativeness of future demand signals. This creates a strategic interaction between pricing, ordering, and learning: the manufacturer can influence the pace of learning through wholesale prices, whereas the retailer internalizes the effect of inventory decisions on future information. We analyze a finite-horizon dynamic game in which a manufacturer sets a wholesale price, the retailer then chooses an order quantity, demand is realized, and both firms observe sales. For Weibull demand with a conjugate prior, we extend a dimensionality-reduction approach from single-agent inventory learning models to a strategic supply-chain setting and use it to establish the existence of a Markov perfect equilibrium. For exponential demand, we further show that the equilibrium is unique and admits a recursive characterization. Our numerical analysis shows that public learning can create conflicting incentives in the supply chain: In order to induce larger orders and reduce future censoring, the manufacturer chooses a wholesale price that is lower than a myopic benchmark. By contrast, because of its forward-looking ordering incentive, the retailer may prefer slower learning to avoid strengthening the manufacturer's future wholesale-pricing position.