This paper extends the theory of N competitive newsvendors to the case where competition occurs simultaneously in price and inventory. The basic research questions are whether the Nash equilibrium exists in this game, whether it is unique, and how the resulting inventories and prices are affected by competition. Using a novel method, we show the quasiconcavity of the competitive newsvendor's problem and establish the existence of the pure–strategy Nash equilibrium. Through a contraction mapping approach, we develop sufficient conditions for the Nash equilibrium to be unique. We then analyze the properties of the equilibrium and compare it with the optimal solution for the (noncompeting) price–sensitive newsvendor. We prove that at a symmetric equilibrium, retail prices and safety stocks strictly increase with the proportion of a newsvendor's unsatisfied customers that switch to a competitor, but strictly decrease with the intensity of price competition. Total inventories, on the other hand, increase with the intensity of price competition. Furthermore, the competitive equilibrium never has lower safety stocks and higher retail prices (a situation that definitely hurts the customers) than the solution for noncompetitive newsvendors.
