  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.

Dynamical Systems