Dynamic Wholesale Pricing under Censored-Demand Learning
This work addresses a strategic learning problem in supply chain management for manufacturers and retailers, offering incremental improvements in equilibrium analysis and computation for specific demand distributions.
The paper tackles the problem of dynamic wholesale pricing between a manufacturer and retailer with censored demand, where only sales are observed, and characterizes Markov perfect equilibria based on a public belief state. For Weibull demand, it extends a scaling approach to prove equilibrium existence and simplifies computation to a one-parameter recursion, while for exponential demand, it shows uniqueness and provides a simple backward recursion for computation.
We study a finite-horizon dynamic wholesale-price contract between a manufacturer and a retailer, both of whom observe only sales, rather than the true demand. When the retailer stocks out, unmet demand is unobserved, so both parties update a common posterior over the demand distribution from sales data. Each period, the manufacturer sets the wholesale price, the retailer chooses an order quantity, and the public belief state is updated. We characterize Markov perfect equilibria as functions of this public belief. Our main results are as follows: for Weibull demand, we extend the well-known scaling approach to this strategic learning setting, prove the existence of an equilibrium, and reduce computation to a standardized one-parameter recursion; for exponential demand, we show that the equilibrium is unique and computable via a simple backward recursion.