When Does the Winner Take All in Two-Sided Markets?

We study the diffusion of competing two-sided networks using a differential game framework. We find that whether the winner takes all depends on the participation behaviour of individual agents on both sides of the market. When individual agents tend to participate in only one network, one network will dominate the market. As the tendency for joining multiple networks increases, the possibility for two networks to co-exist in the long-run also increases. Thus the steady-state market share of competing two-sided networks can be very different depending on adopters' choice of "multi-homing" or "single-homing".