Game theoretic analysis of customer subscription decisions in networks with positive externality

In this paper we build a game-theoretic model that captures the strategic behavior of customers facing a service subscription purchasing decision. We focus on a class of products with positive network effects. Customers interact according to a network structure through which the positive externality is conveyed. We use a one-shot simultaneous incomplete information game to model the interaction of customers and provide an equilibrium in which a customer´s subscription decision depends on her network centrality. Using Banach Fixed Point Theorem, we prove the existence and the uniqueness of the equilibrium and provide an algorithm to compute the equilibrium. Finally, we apply our results to real network data to illustrate the customers´ decisions. We also discuss the convergence of our equilibrium computing algorithm and explain how the steps of algorithm relate to customers´ behavior in reaching the equilibrium in reality.