The hotelling model with capacity precommitment

We consider the two-stage game proposed by Kreps and Scheinkman [83] in the address model of horizontal differentiation developed by Hotelling. Firms choose capacities in the first stage and then compete in price. We show that capacity precommitment softens price competition drastically. In almost all subgame perfect equilibrium, firms behave as if they were an integrated monopoly i.e., choose capacities which exactly cover the market, so that there is no room for price competition at all. The foundation of this result is that capacity precommitment enables firms to take advantage of the local monopoly structure inherent to the Hotelling model. If furthermore the installation cost for capacity is one fourth of the transportation cost, then this result stands for all SPE. We also provide an interesting treatment of mixed strategies equilibria which is quite new in this literature.