Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 2, Pages 119-133

Analytic solutions of nonlinear Cournot duopoly game

Akio Matsumoto1 and Mami Suzuki2

1Department of Economics, Chuo University, 742-1 Higashinakano, Hachiojishi, Tokyo 192-0393, Japan
2Department of Management Informatics, Aichi Gakusen University, 1 Shiotori, Oike-cho, Toyota 474-8532, Japan

Received 12 December 2004

Copyright © 2005 Akio Matsumoto and Mami Suzuki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.