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We study competition in two-sided markets with a common network externality rather those 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 symmetric equilibrium and show that when the externality itself satisfies a homogeneity condition then platforms' profits and price structures have some specific properties. Our results reveal how the rents coming from network externalities are shifted by platforms from one side to the other, according to the homogeneity degree. Prices are affected but in such a way that platforms only transfer rents from consumers to providers. In the specific but realistic case where the common network externality is homogeneous of degree zero, platforms' profits do not depend on the intensity of the (common) network externality. This result differs from those of the two-sided models, which deal with standard positive inter-group network externality.
