Dynamic duopoly with slowly changing customer loyalties

A dynamic model of duopoly is considered in which a fixed fraction of the customer population changes loyalties in each period from the current high-price setter to the current low-price setter. The model is a stochastic game, and it is shown to have a Markov perfect equilibrium with distinctive economic features. Effects of changes in the duopolists' discount factors and in the stickiness of the customer loyalties on the equilibrium strategies and on long-run market structure are studied.