Statistical Dynamics in Piecewise Linear Cournot Game with Heterogeneous Duopolists

We study a Cournot duopoly dynamic model in which reaction functions are piecewise linear. Such a model typically generates ergodic chaos when it involves strong nonlinearites. To investigate statistical properties, we construct explicit forms of density functions associated with chaotic trajectories. We demonstrate that the long-run average behavior possesses regular properties although each chaotic trajectory exhibits irregular motions. In particular, the ratios of the average outputs as well as the average profits are the same as those of Cournot outputs as well as Cournot profits. Acknowledgement An early draft of thie paper was presentd at the Odense conference, Osense, Denmark, May 18-22, 2003. Helpful comments from participants are gretefully acknowledged. The financial supports from Chuo University (Joint Research Grant, 0382) and the Japan Minstry of Education, Culture, Sports, Science and Technology (Grand-in-Aid for Scientific Reseach (B), 14330037) are also acknowledged.