Dynamic price competition in aftermarkets with network effects

This paper studies the dynamic price competition between two firms that sell horizontally differentiated durable goods and, subsequently, provide exclusive complementary goods and services to their customers. The paper analyzes how optimal pricing strategies are affected by the existence of network effects associated with the size of firms' consumer base. The interaction is thoroughly analyzed as a continuous time linear-quadratic differential game. We provide a necessary and sufficient condition for the existence of a unique duopoly equilibrium in affine strategies. When this condition holds, we show that optimal pricing strategies crucially depend on the nature of the network effects.