Aftermarket Power and Basic Market Competition

I revisit the relation between aftermarket power and basic market competition. I consider an infinite period model with overlapping consumers: in each period, one consumer is born and joins one of the existing installed bases, then aftermarket payoffs are received by sellers and consumers, then finally one consumer dies. I derive the unique symmetric Markov equilibrium of this game and the resulting stationary distribution over states (each firm's installed base). I show that an increase in aftermarket power increases the extent of increasing dominance (i.e., a large firm is increasingly more likely to capture a new consumer than a small firm). This in turn leads to several implications of aftermarket power. First, the stationary distribution places greater weight on asymmetric states. Second, social welfare is greater. Third, under some conditions consumer welfare is also greater. Fourth, the value of a firm with zero installed base is lower, and so barriers to entry are higher.