This paper investigates how firms should select their production sites and quantities under rivalry. There are assumed to be a finite number of discrete potential location sites, and a finite number of discrete markets, which may or may not coincide. Firms first decide either simultaneously or sequentially whether and where to establish a production site. The fixed cost of opening a facility and the marginal cost of production both depend on where the facility is located.
Firms then choose a production quantity for each market.
Prices in each market are determined by the total quantity available at that location. The formulation thus corresponds to a multi-market, oligopolistic spatial competition with heterogeneity in production and logistic costs. We analyze the pure-strategy Nash equilibria of the game. We show that Nash equilibria always exists if firms enter sequentially. We provide sufficient conditions for the existence of Nash equilibria in the simultaneous entry game.