Complex dynamics and control investigation of a Cournot triopoly game formed based on a log-concave demand function

This article investigates the dynamics of a Cournot triopoly game whose demand function is characterized by log-concavity. The game is formed using the bounded rationality approach. The existence and local stability of steady states of the game are analyzed. We find that an increase in the game parameters out of the stability region destabilizes the Cournot-Nash steady state. We confirm our obtained results using some numerical simulation. The simulation shows the consistence with the theoretical analysis and displays new and interesting dynamic behaviors, including bifurcation diagrams, phase portraits, maximal Lyapunov exponent, and sensitive dependence on initial conditions. Finally, a feedback control scheme is adopted to overcome the uncontrollable behavior of the game's system occurred due to chaos.