THE EXISTENCE OF EQUILIBRIUM IN A DIFFERENTIATED DUOPOLY WITH NETWORK EXTERNALITIES*

The existence of a pure‐strategy subgame‐perfect equilibrium in qualities and prices is investigated in a duopoly model of vertical differentiation where quality improvements require a quadratic variable cost and network externalities operate. We show that there exists a parameter region where the incentive to predate at the quality stage prevents firms from reaching a pure‐strategy non‐cooperative equilibrium with prices above marginal costs. If network externalities are sufficiently large, a Bertrand equilibrium with zero profits may arise, although the amount of product differentiation is strictly positive.