Multistability and cyclic attractors in duopoly games

✍ Scribed by Gian Italo Bischi; Cristiana Mammana; Laura Gardini

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 981 KB
• Volume: 11
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00130-1

✦ Synopsis

A dynamic Cournot duopoly game, whose time evolution is modeled by the iteration of a map X xY y 3 r 1 yY r 2 x, is considered. Results on the existence of cycles and more complex attractors are given, based on the study of the one-dimensional map p x r 1 r 2 x. The property of multistability, i.e. the existence of many coexisting attractors (that may be cycles or cyclic chaotic sets), is proved to be a characteristic property of such games. The problem of the delimitation of the attractors and of their basins is studied. These general results are applied to the study of a particular duopoly game, proposed in M. Kopel [Chaos, Solitons & Fractals, 7 (12) (1996) 2031±2048] as a model of an economic system, in which the reaction functions r 1 and r 2 are logistic maps.