©2006 INFORMS A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model

This paper studies a one-shot inventory replenishment problem with dynamic pricing. The customer arrival rate is assumed to follow a geometric Brownian motion. Homogeneous customers have an isoelastic demand function and do not behave strategically. We find a closed-form optimal pricing policy, which utilizes current demand information. Under this pricing policy the inventory trajectory is deterministic, and a retailer sells all inventory. We show that dynamic pricing coordinated with the inventory decision achieves significantly higher profits than does static pricing. Furthermore, under oligopolistic competition we establish a weak perfect Bayesian equilibrium for the price and inventory replenishment game. We find the pricing equilibrium to be cooperative even in a noncooperative environment, but that inventory competition results in overstock and damages profits. Finally, we examine the trade-off between dynamic pricing and price precommitment and find that flexible pricing is still beneficial, provided competition is not too intense. Subject classifications: differential games; dynamic pricing; geometric Brownian motion; martingales; revenue management