We develop a two-sided market model where both platforms and sellers charge buyers for access. When network effects are moderate, a dominant platform that attracts more sellers and buyers is more likely to arise. Compared to when platforms split the market equally, a dominant platform always leads to higher consumer surplus and total welfare. Moreover, both of these measures improve as network effects increase. Our results suggest that competition authorities should be cautious regarding complaints related to dominant platforms in two-sided markets, as they may be good for consumers.