The choice of network compatibility in two-sided markets

I consider a duopolistic platform competition in which (i) platforms are viewed as heterogeneous by both groups of agents, and sellers can choose multiple platforms; (ii) buyers have a network benefit from their own platform, and a partial network benefit from platform compatibility; and (iii) platforms determine the degree of network compatibility by Nash bargaining. In symmetric equilibrium, the degree of network compatibility increases when the degree of network effect increases or the degree of differentiation of the platform for sellers decreases. Moreover, it is excessive from a social planner's viewpoint, and incompatibility is desirable for consumers.