Dynamic Wholesale Pricing under Censored-Demand Learning

2026-03-13

AI Summary

This study addresses a finite-horizon dynamic game between a manufacturer and a retailer who observe only censored sales data (i.e., truncated demand) and sequentially set wholesale prices and order quantities by sharing Bayesian posterior beliefs, aiming to achieve a Markov perfect equilibrium. The paper extends classical scaling techniques to the setting of strategic learning under censored demand and, for the first time, establishes computable equilibrium structures for Weibull and exponential demand distributions. For Weibull demand, the existence of equilibrium is proven and reduced to a single-parameter recursive formulation; for exponential demand, equilibrium uniqueness is established, and an efficient backward recursion algorithm is provided for its computation.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• dynamic wholesale pricing
• censored demand
• demand learning
• Markov perfect equilibrium
• inventory management

Innovation

• censored-demand learning
• dynamic wholesale pricing
• Markov perfect equilibrium
• Bayesian updating
• scaling approach