Market coverage and the existence of equilibrium in a vertically differentiated duopoly

We consider a duopoly model of product differentiation with quadratic costs of quality improvements, so that the finiteness property does not hold. We investigate the existence and characterisation of pure strategy subgame perfect equilibria for fixed market size. The alternative cases of full and partial market coverage are considered. We show that the parameter intervals in which the two alternative regimes can arise are disjoint. Our findings reveal that in such interval of demand parameters, a pure strategy equilibrium fail to exist.