An oligopoly model with best response and imitation rules

Abstract

Imitation-based behaviors are considered in economics with significant contributions in reference to homogeneous populations where players are characterized by the same decisional processes (see for example [42,48]). However, the presence of imitation behaviors is detected in experimental oligopolies coexisting with rational-like rules. This motivates us to consider an heterogeneous population where best responders and imitators coexist and compete in a deterministic oligopoly framework. The model we formulate is characterized by two stationary states, specifically the Cournot–Nash equilibrium and a further production level at which best responders are inactive and imitators produce at the marked clearing price. The heterogeneities among players give to the model a nonlinear structure, influence the stability properties of the Cournot–Nash equilibrium and give rise to complex dynamic scenarios. We found that the imitators’ relative fraction have an ambiguous role in determining the stability properties of the Cournot–Nash equilibrium and, provided intermediate values of the population size, its variations may cause the occurrence of both flip and Neimark–Sacker bifurcations. Chaotic dynamics and coexistent attractors, characterized by not connected basins, may also be observed. We finally note that certain dynamic regimes, described by the model, are provided by analogous features as those characterizing experimental outcomes and several experiments can be reproduced with different parameters’ sets.