Cournot equilibrium in case of \((-1)\)-concave price function. (English) Zbl 1513.91040
Summary: 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.
MSC:
91B54 | Special types of economic markets (including Cournot, Bertrand) |
91B52 | Special types of economic equilibria |
91A80 | Applications of game theory |