Oligopolistic competition: Dynamic analysis and chaos control

Abstract

In oligopolistic markets, firms offer homogeneous or differentiated products. The Cournot and Bertrand models are the two classical frameworks used to describe competition in such markets. In the Cournot model, firms maximize their profits by choosing production quantities while taking their competitors’ decisions into account. In the Bertrand model, firms maximize their profits by choosing prices while considering the pricing strategies of their competitors. The aim of this thesis is to develop and analyze discrete time oligopoly models based on realistic assumptions regarding firms’ expectations and bounded rationality. The qualitative behavior of these models is investigated using stability and bifurcation theory. Particular attention is devoted to the emergence of complex dynamics, including periodic oscillations and chaotic behavior, resulting from variations in key model parameters. Several numerical tools, including bifurcation diagrams, phase portraits, and Lyapunov exponents, are employed to characterize the system dynamics and identify transitions from stability to chaos. Finally, different chaos control strategies are implemented to suppress unstable and chaotic trajectories and stabilize economically meaningful equilibria, thereby improving the predictability and reliability of the proposed models.