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

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.