Duopoly competition in a service market with strategic heterogeneous customers and servers

This paper analyzes duopoly competition between service providers when the demand is segments so that each segment prefers a certain server if prices were equal. For example, a customer needs to choose between two hospitals where one of them is closer than the other. We are interested in the interaction between the service providers, the resulting price equilibrium, and conditions for each of them to act as a monopoly. The analysis consists of two steps. First, we compute the (unique) equilibrium joining (and balking) strategies of customers given the service fees set by the servers. We present five types of equilibria when customers do not balk and twelve additional types when balking is implemented. Using this customer behavior, we compute the duopoly price equilibrium.