Mathematical Formulation and Analysis of the Optimal Launch Timing for Mobile Applications with Perceived Value and Network Effect

Abstract

Successive release is a common strategy adopted by mobile app providers, and determining the launch timing of new app versions presents an important challenge to these providers. Network effect and consumers' perceived value are significant factors that influence the decisions of providers. By focusing on a monopoly market, we develop an optimization model that incorporates the two factors to determine the optimal launch timing of new versions of mobile apps. The model is solved by Lagrangian method, and the closed-form results indicate that the monopoly provider launches new app versions as soon as possible if the consumers' perceived value is not sufficiently high. Otherwise, the new version is launched after (or before) the sales of its former version reach maturity if the network effect is (or not) sufficiently high. Moreover, the monopoly app vendor delays the launch of a new version when the consumers enjoy a large network externality; however, the same vendor accelerates the release of upgrades if the consumers have a high perceived value of the app. This paper presents a novel mathematical formulation to analyze the launching policy of digital products.