On extensive dynamics of a Cournot heterogeneous model with optimal response

Abstract

The objective of this paper is the study of the dynamical properties analysis of an original specification of the classical Cournot heterogeneous model with optimal response; specifically, a new approach that considers ordinal utility instead of cardinal monetary amounts is proposed where the classical decision of quantity is disentangled from the decision on imitation. The analysis is performed by means of bifurcation diagrams, the 0-1 test for chaos, power spectral density, histograms, and trajectory analysis. For this purpose, a new perturbation parameter ε of the initial condition is introduced, and together with the intensity of choice parameter β determining the share of responders vs imitators, the system is researched. Depending on ε and β, extreme reach dynamics, and coexisting attractors, periodic and chaotic trajectories are investigated through massive simulations. Those dynamics represent alternation between stability, cycles and chaos in the market. As the dynamics are completely endogenous, it means that swings in economy are intrinsic to the system and that they may persist unless controlled.