Service segment competition: size or value, which matters?

We study a service market with two firms: one that provides regular and another that provides premium services. Customers are delay sensitive and heterogeneous in evaluating the service level. We study two competition games that differ in segmentation-marketing strategies. One is the size-based competition in which firms compete on the segment size dimension, and the other is the value-based competition in which firms compete on the segment target (regarding customer valuation) dimension. For both games, the Nash equilibrium always exists, and the (Pareto dominant) equilibrium is unique. Interestingly, the premium service provider's effective arrival rate can be increasing in its competitor's service rate in the value-based game. Moreover, we capture the conditions for the equilibrium market as either a monopoly or a duopoly and show that size-based competition helps sustain service variety. We also show that the prices are reduced in the value-based game; the premium (regular) service provider serves more (fewer) customers in the value-based game than in the size-based game. Our results show that value-based competition is more intensive in the sense that the number of customers who are served, customer surplus and social welfare are higher, while the total revenue of two firms is lower in the value-based competition than in the size-based competition.