Uniqueness results and algorithm for Stackelberg-Cournot-Nash equilibria

This paper uses recently developed theory of sensitivity analysis to explore the reaction of a Cournot-Nash equilibrium to a Stackelberg firm, and to analyze the effect of this reaction on the uniqueness of the Stackelberg-Cournot-Nash equilibrium. Some of the results presented are not new, but the methods used provide simpler proofs and a different perspective. More importantly, the methods used here allow the development of new conditions for a unique Stackelberg-Cournot-Nash equilibrium that extends those previously known. The methods used also provide for the development of an efficient algorithm for finding the equilibrium.