Chaotic dynamics in three dimensions: a topological proof for a triopoly game model

2013/01/31 by Pireddu, Marina
#37B10 #37N40 #54H20 #54H25 #91B55 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.7556

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 Poincaré-Miranda Theorem and on the properties of the cutting surfaces.

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