Chaotic dynamics in three dimensions: a topological proof for a triopoly game model
Dynamical Systems
2013-02-01 v1
Abstract
We rigorously prove the existence of chaotic dynamics for the triopoly game model already studied, mainly from a numerical viewpoint, in the working paper by Naimzada and Tramontana [2011]. 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 in Pireddu and Zanolin [2007], based on the Poincar\'e-Miranda Theorem and on the properties of the cutting surfaces.
Keywords
Cite
@article{arxiv.1301.7556,
title = {Chaotic dynamics in three dimensions: a topological proof for a triopoly game model},
author = {Marina Pireddu},
journal= {arXiv preprint arXiv:1301.7556},
year = {2013}
}
Comments
21 pages, 7 figures