We propose a general model of oligopoly with firms relying on a two factors production function. The factors are chosen sequentially. In a first stage, firms choose the level of the fixed factor. In a second stage, firms compete in price, and determine the level of variable factor necessary required to satisfy the whole demand.
This setting generalizes the notion of capacity constraint. When the production function allows a certain degree of substitutability, the capacity constraint is “soft”, implying a convex and smooth cost function in the second stage.
We show that there exists a unique equilibrium prediction for the game, whatever the returns to scale. This equilibrium is characterized by a high level for price. We provide simulations, demonstrating non-standard results on the effects of the number of firms on the market price and welfare.