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 appears in consumer utility. Full market coverage is assumed. We show that the incentive to predate prevents firms to reach a pure strategy noncooperative 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. If the weight of network externalities exceeds that of hedonic satisfaction in consumer preferences, then predation is always a dominant strategy