TSYS School's Lydia Ray Contributes to Development of Formal Duopoly Model Explaining Software Pricing and Profits in the Presence of Bugs

New research by TSYS School computer scientist Lydia Ray along with Ramakanta Patra of Cardiff Metropolitan University, Debapriya Sen of Toronto Metropolitan University and Giorgos Stamatopoulos of the University of Crete studies a duopoly model of product competition between a proprietary firm and an open-source firm that each sell the same product, but of different kinds. Within their model there is a probability that each product can suffer damage (“a bug”), such that for the proprietary product, the bug can be only internally fixed by the firm during its next product upgrade. In contrast, for the open-source product, the bug can be fixed by end users (consumers) and the probability of fixing the problem increases as more consumers purchase the open-source product. Ray and her colleagues model two segments of consumers: a segment of low-technical consumers who always buys the proprietary product and another segment of high-technical consumers who are distributed in the Hotelling linear city unit interval with two firms at the end points. It is shown that when the damage to the product caused by an adverse event is minor, in the unique equilibrium outcome the proprietary firm serves both segments of consumers, sets a higher price and obtains a higher profit. In contrast, when the damage to the product caused by an adverse event is of moderate magnitude, in the unique equilibrium outcome the two firms are local monopolists in two segments. Moreover, in this case the open-source firm sets a higher price and obtains a higher profit.