Does the Absence of Competition in the Market Foster Competition for the Market? A Dynamic Approach to Aftermarkets

In this paper, we investigate dynamic price competition when firms strategically interact in two distinct but interrelated markets: a primary market and an aftermarket, where indirect network effects arise. We set up a differential game of two-dimensional price competition and we conclude that the absence of price competition in the aftermarket (competition in the market) fosters dynamic price competition in the primary market (competition for the market). We also investigate the impact of network sizes on firms' prices in the primary market concluding that, in equilibrium, larger firms have incentives to compete more fiercely for new "uncolonized" consumers.