Ee. Schlee, A CURVATURE CONDITION ENSURING UNIQUENESS OF COURNOT EQUILIBRIUM, WITH APPLICATIONS TO COMPARATIVE STATICS, Economics letters, 41(1), 1993, pp. 29-33
We study a curvature condition on demands that, with a cost assumption
, ensures the uniqueness of Cournot equilibrium. For two firms, the co
ndition is that industry marginal revenue rises no faster than price f
alls. The condition is weaker with more firms, and holds for any smoot
h demand curve, provided there are enough firms.