Cournot equilibrium in case of (-1)-concave price function

Abstract

We consider a class of homogeneous Cournot oligopolies with (−1)concave price function. We show some useful properties of the revenue function in case of (−1)-concave price function and prove the existence of an equilibrium in the continuous and non-differentiable case. A simple proof of an equilibrium uniqueness result in the smooth case with (−1)/N-concave (N-number of the firms in the market) price function is provided.