We study competition in two sided markets with common network externality rather than with the standard inter-group effects. This type of externality occurs when both groups benefit, possibly with different intensities, from an increase in the size of one group and from a decrease in the size of the other. We explain why common externality is relevant for the health and education sectors. We focus on the symmetric equilibrium and show that when the externality itself satisfies an homogeneity condition then platforms’ profits and price structure have some specific properties. Our results reveal how the rents coming from network externalities are shifted by platforms from one side to other, according to the homogeneity degree. In the specific but realistic case where the common network externality is homogeneous of degree zero, platform's profit do not depend on the intensity of the (common) network externality. This is in sharp contrast to conventional results stating that the presence of network externalities in a two-sided market structure increases the intensity of competition when the externality is positive (and decreases it when the externality is negative). Prices are affected but in such a way that platforms only transfer rents from consumers to providers.