When Stackelberg and Cournot Equilibria Coincide

Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria

Stackelberg versus Cournot Equilibrium

We reconsider Stackelberg’s classical critique of the Cournot duopoly, in the framework of endogenous timing for two-player games. For quantity duopoly we provide different sets of minimal conditions, directly on the demand and cost functions, yielding respectively the simultaneous and the two sequential modes of play. While our findings essentially confirm the predominance of the former, they ...

On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation

We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot–Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot– Nash outcome and one ...

Two Remarks on Cournot Equilibria

Making the weak assumption that the left-hand side of this equation is downward sloping, there will be a unique Y that solves this equation, which depends only on the sum of the marginal costs, not on their distribution across the firms. The observation that output and price in a Cournot industry is independent of the distribution of marginal costs has undoubtably been noted and used several ti...

Optimal Transport and Cournot-Nash Equilibria

Abstract We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results and a characterisation of equilib...