Computing topological entropy in asymmetric Cournot duopoly games with homogeneous expectations

Abstract

The main aim of this paper is to analyse the dynamics of nonlinear discrete-time maps generated by duopoly games in which players have homogeneous expectations and heterogenous nonlinear cost functions. This framework leads to reaction functions that are non-monotonic and asymmetric and, in the particular case of naïve expectations, the model takes the form of an anti-triangular map, $T(x, y) = (f(y), g(x))$ characterized by a rich dynamical behavior, from stable to chaotic Nash equilibria. We also present the computation of topological entropy of this nonlinear Cournot model by using tools from symbolic dynamics and tensor products.