Chaotic dynamics in three dimensions: A topological proof for a triopoly game model. (October 2015)

• Record Type: Journal Article
• Authors: Pireddu, Marina
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 79
• Page End: 95
• Publication Date: 2015-10
• Subjects: Chaotic dynamics -- Stretching along the paths -- Triopoly games -- Heterogeneous players; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.03.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We rigorously prove the existence of chaotic dynamics for a triopoly game model. In the model considered, the three firms are heterogeneous and in fact each of them adopts a different decisional mechanism, i.e., linear approximation, best response and gradient mechanisms, respectively. The method we employ is the so-called "Stretching Along the Paths" (SAP) technique, based on the Poincaré–Miranda Theorem and on the properties of the cutting surfaces.