Asymmetric Bertrand-Edgeworth-Chamberlin Competition with Linear Demand: A Pediatric Vaccine Pricing Model

Abstract

Pricing strategies in the U.S. pediatric vaccines market are studied using a Bertrand-Edgeworth-Chamberlin price game. The game analyzes the competition between asymmetric manufacturers with limited production capacities and linear demand, producing differentiated products. The model completely characterizes the unique pure strategy equilibrium in the Bertrand-Edgeworth-Chamberlin competition in an oligopoly setting. In addition, the complete characterization of mixed strategy equilibrium is provided for a duopoly setting. The results indicate that the pure strategy equilibrium exists if the production capacity of a manufacturer is at their extreme. For the capacity regions where no pure strategy equilibrium exists, there exists a mixed strategy equilibrium. A duopoly setting provides the distribution functions of the mixed strategy equilibrium for both manufacturers. The proposed game is applied to the U.S. pediatric vaccine market, in which a few asymmetric vaccine manufacturers produce differentiated vaccines. The source of differentiation in the competing vaccines is the number of medically adverse events, the number of different antigens, and special advantages of those vaccines. The results indicate that the public sector prices of the vaccines are higher than the vaccine equilibrium prices. Furthermore, the situation when shortages of certain pediatric vaccines occur is studied. Market demand and degree of product differentiation are shown as two key factors in computing the equilibrium prices of the vaccines.