Negative intra-group externalities in two-sided markets

Two types of agents interact on a pre-existing free platform. Agents value positively the presence of agents of the other type but may value negatively the presence of agents of their own type. We ask whether a new platform can find fees and subsidies so as to divert agents from the existing platform and make a profit. We show that this might be impossible if intra-group negative externalities are sufficiently (but not too) strong with respect to positive inter-group externalities.