Collusion and Network Effects: Modeling the Dynamics of Single- and Multi-Sided Platforms

In this paper we apply a general model of one-sided and two-sided platform businesses to a collusive framework which we model as joint profit maximization. We have a particular interest in how the social loss and other metrics depend on the strength of the network (direct or indirect) effect. We study how network effects impact the optimal collusive configuration, how that configuration compares to socially optimal .configurations, and how the deadweight loss decomposes between market power and the unpriced network externality. We find that full collusion (in the sense of joint profit maximization, acting as one single firm) is unlikely to develop if network effects are even moderately strong, since the optimal configuration requires one of the platforms to either be very small or, usually, to shut down altogether. Of course it remains possible that other forms of mutually beneficial coordination might still obtain. We further find that even when able to perfectly price discriminate for or against multi-homing subscribers, neither colluders nor planners meaningfully benefit from that option.