Stackelberg versus Cournot: A differential game approach

We propose an infinite-horizon differential oligopoly game where, at each point in time, m Stackelberg leaders and n−m Stackelberg followers exploit a common-pool renewable resource and sell their harvest in the marketplace at a price that depends on total harvest. We derive a feedback-generalized-Stackelberg–Nash–Cournot equilibrium (a generalization of the feedback Stackelberg equilibrium), nesting feedback Stackelberg and feedback Cournot as special cases. We proceed with a comparison between the feedback Stackelberg and the feedback Cournot equilibria, and find a number of interesting results in contrast with “static” oligopoly theory. As to the relative efficiency of the two equilibria, we show that the Cournot equilibrium can be more efficient than the Stackelberg equilibrium. This holds true in the short-run, at the steady-state, and in terms of discounted welfare.