Influence of rationality levels on dynamics of heterogeneous Cournot duopolists with quadratic costs

TL;DR

This paper analyzes how different rationality levels among duopoly players affect the stability and dynamics of their competition, revealing counterintuitive effects on stability regions and complex behaviors.

Contribution

It introduces a new symbolic computation approach to establish stability conditions and explores the impact of rationality levels on bifurcations in heterogeneous Cournot duopoly models.

Findings

Stability region is smallest when the second player is rational.

Largest stability region occurs when the second player is boundedly rational.

Complex dynamics such as strange attractors can emerge in the models.

Abstract

This paper is intended to investigate the dynamics of heterogeneous Cournot duopoly games, where the first players adopt identical gradient adjustment mechanisms but the second players are endowed with distinct rationality levels. Based on tools of symbolic computations, we introduce a new approach and use it to establish rigorous conditions of the local stability for these models. We analytically investigate the bifurcations and prove that the period-doubling bifurcation is the only possible bifurcation that may occur for all the considered models. The most important finding of our study is regarding the influence of players' rational levels on the stability of heterogeneous duopolistic competition. It is derived that the stability region of the model where the second firm is rational is the smallest, while that of the one where the second firm is boundedly rational is the largest. This fact is counterintuitive and contrasts with relative conclusions in the existing literature. Furthermore, we also provide numerical simulations to demonstrate the emergence of complex dynamics such as periodic solutions with different orders and strange attractors.