A general model of oligopoly endogenizing Cournot, Bertrand, Stackelberg, and Allaz-Vila

This paper analyzes a T-stage model of oligopoly where firms build up capacity and conclude forward sales in stages t<T, and they choose production quantities in t=T. We consider the case of n firms with asymmetric marginal costs. In the two-stage game, the set of outcomes is a quasi-hyperrectangle including Cournot, Allaz-Vila, and all two-stage Stackelberg outcomes. In general, it consists of T-1 such hyperrectangles where the lower bound approaches the Bertrand outcome as T tends to infinity. In the limit, a range of outcomes stretching from Cournot via Stackelberg to Bertrand can result in equilibrium, i.e. the mode of competition is entirely endogenous.