A Model of Market Power in Customer Markets

We develop a model for studying dynamic competition in environments with frictions that lead to partial lock-in of customers to products. The dynamic aspects associated with customer retention and acquisition introduce pricing incentives that do not exist in more traditional, static product markets. The proposed model, while highly stylized, maintains certain symmetry properties that allow us to obtain equilibrium existence and uniqueness. We then study the comparative statics of the model and derive a closed-form relationship between average equilibrium markups and the Herfindahl index. We illustrate how the model can be used by analyzing mergers in such a dynamic environment.