On the endogeneity of Cournot, Bertrand, and Stackelberg competition in oligopolies

In many industries, firms pre-order input and forward sell output prior to the actual production period. It is known that forward buying input induces a “Cournot–Stackelberg endogeneity” (both Cournot and Stackelberg outcomes may result in equilibrium) and forward selling output induces a convergence to the Bertrand solution. I analyze the generalized model where firms pre-order input and forward sell output. First, I consider oligopolists producing homogenous goods, generalize the Cournot–Stackelberg endogeneity to oligopoly, and show that it additionally includes Bertrand in the generalized model. This shows that the “mode of competition” between firms may be entirely endogenous. Second, I consider duopolies producing heterogenous goods. The set of equilibrium outcomes is characterized and shown not to contain the Bertrand solution anymore. Yet, forward sales increase welfare also in this case, notably even when goods are complements.