Market Coverage and the Existence of Equilibrium in a Vertically Differentiated Duopoly

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. The alternative cases of partial and full market coverage are considered. It is shown that there exists a parameter range where the incentive to decrease differentiation arises for the high-quality firm, preventing firms to reach a pure-strategy duopoly equilibrium.