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 prices. We show that price competition is drastically softened since in almost all subgame perfect equilibria firms behave as if they were an integrated monopolist i.e., they choose capacities which exactly cover the market, so that there is no room for price competition. If furthermore the installation cost for capacity is one fourth of the transportation or more, this result stands for all SPE. Like Kreps and Scheinkman, we show that the Cournot allocations coincide with the SPE allocations of our game form. Finally, our analysis provides an interesting treatment of mixed strategy equilibria which is quite new in the literature.