Controlling the Cournot-Nash Chaos

The recently developing theory of nonlinear dynamics shows that any economic model can generate a complex dynamics involving chaos if the nonlinearities become strong enough. This study constructs a nonlinear Cournot duopoly model, reveals conditions for the occurrence of chaos, and then considers how to control chaos. The main purpose of this paper is to demonstrate that chaos generated in Cournot competition is in a double bind from the long-run perspective: a firm with a lower marginal production cost prefers a stable (i.e., controlled) market to a chaotic (i.e., uncontrolled) market, while a firm with a higher marginal cost prefers the chaotic market. Helpful remarks and comments by Ferenc Szidarovszky, Michael Kopel, Shahriai Yousefi, and three anonymous referees are gratefully acknowledged. Financial support from the Japan Ministry of Education, Culture, Sports, Science, and Technology, Grant-in-Aid for Scientific Research (B)15330037, and from Chuo University, Joint Research Grant 0382, is highly appreciated.