Vertical differentiation, network externalities and compatibility decisions: an alternative approach

We characterize the equilibrium of a game in vertically differentiated market which exhibits network externalities. There are two firms, an incumbent and a potential entrant. Compatibility means in our model that the inherent qualities of the goods are close enough. By choosing its quality, the entrant chooses in the same time to be compatible or not. The maximal quality difference that allows compatibility i.e the compatibility interval is chosen by the incumbent which involves costs increasing with the width of that interval. We show that in order to have two active firms at price equilibrium, the sufficient condition on the market size of a standard vertical differentiation model remains valid under compatibility. However, an additional condition on the firms' qualities is needed under incompatibility. For a small quality segment, the incumbent can block entry choosing an empty compatibility interval. At the subgame perfect equilibrium, incompatibility prevails if the quality segment is large and the compatibility costs are high. Compatibility prevails for sufficiently large quality segments and low costs of compatibility. Finally there is no entry if the quality segment is small and the compatibility costs are high.