Dynamic Wholesale Pricing under Censored-Demand Learning

TL;DR

This paper analyzes a dynamic wholesale pricing game with censored demand data, developing equilibrium characterizations and computational methods for Weibull and exponential demand distributions.

Contribution

It extends strategic learning models to censored demand scenarios, providing equilibrium existence, uniqueness, and computational techniques for specific demand distributions.

Findings

Equilibrium characterized as functions of public belief state.

Existence of equilibrium proved for Weibull demand.

Unique equilibrium computable via backward recursion for exponential demand.

Abstract

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.