Price competition in a differentiated products duopoly under network effects

We examine price competition under product-specific network effects, in a duopoly where the products are differentiated both horizontally and vertically. We emphasize the role of consumers' expectations formation. When expectations are not influenced by prices, the market may be shared but shares must be equal unless product qualities differ or one firm, possibly even the low-quality one, may capture the entire market. When expectations are influenced by prices, which would be the case when there is commitment, competition becomes more intense and the high-quality firm tends to capture a larger market share. Under strong network effects there is a continuum of equilibria and the higher the prices, the smaller the difference between those prices can be. Requiring continuity of expectations, however, delivers a unique equilibrium where one firm captures the entire market.