Quality differentiation if market share matters

Using a vertical differentiation model, we investigate the product quality strategies of two competing firms maximizing market shares. The firms are facing variable costs of quality improvement and choose their prices under the constraint of nonnegative profits. We show that in equilibrium there is no differentiation in quality if the market coverage is either increasing or decreasing and concave in quality. Otherwise the existence of an equilibrium depends on the structure of the game. If the firms choose their qualities simultaneously there is no equilibrium, while there is an equilibrium with a first mover advantage and quality differentiation in the sequential quality competition.