Vertical product differentiation and two-sided markets

We model platform competition in a market where products are characterized by cross network externalities. Consumers differ in their valuation of these externalities. Although the exogenous set-up is entirely symmetric, we show that platform competition induces a vertical differentiation structure that allows for the co-existence of asymmetric platforms in equilibrium. We establish this result in two set-ups: in the first one platforms commit to prices, in the second one they commit to network sizes.