Prices, capacities and service quality in a congestible Bertrand duopoly

We study the duopolistic interaction between congestible facilities that supply perfect substitutes. Firms are assumed to make sequential decisions on capacities and prices. Since the outcomes directly affect consumers' time cost of accessing or using a facility, the capacity sharing rule is endogenous. We study this two-stage game for different firm objectives and compare the duopoly outcomes with those under monopoly and at the social optimum. For the symmetrical duopoly outcome, our findings include the following. First, for profit maximizing firms both capacity provision and service quality are distorted under duopoly: they are below the socially optimal levels. This contrasts with the monopoly outcome, where pricing and capacity provision are such that the monopolist does provide the socially optimal level of service quality. Second, duopoly prices are lower than monopoly prices, but higher than in the social optimum. Hence, while price competition between duopolists yields benefits for consumer, capacity competition is harmful. Third, price-capacity competition implies that higher capacity costs may lead to higher profits for both facilities. Finally, if firms care about output as well as profits, this mainly affects pricing behavior; strategic interactions in capacities are much less affected. Finally, we explore the conditions under which symmetrical and asymmetrical duopoly equilibria arise and when they are stable.