We propose a tractable model of asymmetric platform oligopoly in which users from two distinct groups are subject to within-group and cross-group network effects and decide which platform to join. We characterize the equilibrium when platforms manage user access by setting participation fees. We explore the effects of platform entry, change of incumbent platforms’ quality under free entry, and partial compatibility on market outcomes. We show how the analysis can be extended to partial user participation and zero fees for one of the user groups.