Discrete Dynamics in Nature and Society 
Volume 2005 (2005), Issue 2, Pages 119-133
doi:10.1155/DDNS.2005.119

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

Abstract

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.