The Bertrand Duopoly model for demand in economics is a well-used model. Although this model has important insights towards pricing strategy, it does not accurately depict true market behaviors. In this paper, we will examine the advantages and disadvantages of the current model and its assumptions.We then take a whole new approach towards modeling this phenomena, using Poisson processes to model the demand of goods. We will discuss why this is a better approach and explain how we can extend this to better understand pricing strategies and market dynamics. We then apply our findings to the newsvendor problem, a commonly used problem in inventory management. Using non-homogeneous Poisson processes we explain how to find an optimal pricing strategy and an optimal inventory level for the newsvendor problem.In this paper we explain how to extend the newsvendor problem to a newsvendor duopoly problem. Again we show how to find the optimal pricing strategies and inventory levels for multiple goods in a market. Having found the optimal pricing strategy and inventory level, we then examine the market dynamics in more details. We explore monopolistic and duopolistic markets where the goods range from complements to substitutes and homogeneous to differentiated goods. We discuss how to model the progression of the inventory probabilities and then explain how to price inventory options.



College and Department

Physical and Mathematical Sciences; Mathematics



Date Submitted


Document Type





Poisson rates, inventory options, inventory management, dynamic pricing, opti- mal inventory, newsvendor problem

Included in

Mathematics Commons