Partial compatibility in two-sided markets: Equilibrium and welfare analysis

We consider platforms' choices of application compatibility in a two-sided market with single-homing users and multihoming content providers. As the network effect on the user side becomes stronger than on the content provider side, platforms find it more profitable to adopt compatibility. We show that partial compatibility, where some platforms are compatible with each other but not with others, can be a unique coalition-proof market outcome. Still, when the relative network effect is high, the coalition-proof market outcome changes directly from full compatibility to incompatibility as the cost of compatibility technology increases, bypassing partial compatibility. Moreover, consumer and total surpluses can be the highest under partial compatibility, suggesting that promoting compatibility is not always socially optimal.