Claude D'Aspremont, Alexis Jacquemin, Jean Jaskold Gabszewicz, John A. Weymark, On the Stability of Collusive Price Leadership, The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 16, No. 1 (Feb., 1983), pp. 17-25
d’Aspremont et al. (Tue,) studied this question.