BERTRAND-EDGEWORTH DUOPOLY WITH PROPORTIONAL RESIDUAL DEMAND

A complete characterization is given for the prices charged by Bertrand-Edgeworth duopolists with capacity constraints. In general, for the game in which firms' strategy spaces consist of price offers, Nash equilibrium involves nondegenerate mixed strategies. Equilibria never extend below the highest competitive price. With two firms, the Bertrand-Edgeworth model displays a bias for the highest of several market clearing prices. Moreover, these strategies never stop short of the lowest monopoly price. If firms are of unequal size, the larger firm assigns positive probability to a monopoly price, possibly even to several monopoly prices.