Interconnection Incentives of a Large Network

This paper builds on Cremer, Rey and Tirole's analysis of the possible incentives of a firm with the largest share of installed-base customers, in a market characterized by strong network externalities, to degrade or refuse interconnection with its smaller rivals in order to gain a relative quality advantage in competing for new customers. We straightforwardly extend their model to allow any number of smaller symmetric rivals, and we show that if interconnection is degraded the equilibrium can involve tipping away from the largest network even if it has more than half the installed base. Such tipping becomes more likely, for a given initial market share of the largest network, as the number of rivals increases. We examine the minimal market share required for the large firm to choose degradation, whether it leads to an interior equilibrium or a tipping equilibrium, as a function of the model's key parameters. Besides the number of rivals, the key parameters include firms' common marginal cost, and the size of the installed-base relative to potential additional demand. Lower values of these parameters make degradation less likely to be profitable. In the case of the Internet, plausible parameter values suggest that degradation is unlikely to be profitable unless the largest network commands significantly more than fifty percent of the installed customer base.