Bifurcation Analysis of a Cournot Triopoly Game with Bounded Rationality and Chaos Control Via the OGY Method
Résumé
In this study, we explore the dynamics of a triopoly game involving rms with bounded rationality. Our analysis examines the existence and stability of equilibrium points, with a specic focus on the Nash equilibrium point. We found that an increase in the parameters k1 (adjustment speed) and a1 (product substitution) destabilizes the system, leading to more chaotic behavior through flip and Neimark{Sacker bifurcations. This chaotic behavior is examined through numerical simulations, where various parameters are adjusted to observe their eects. The basins of attraction are analyzed, revealing that the basin of attraction varies as the parameter k1 increases. Our approach aims to control the chaotic behavior and stabilize the system by employing the OGY method. Importantly, our analysis emphasizes that the product substitution parameter a1 is a key factor in achieving stabilization within the game. To clearly illustrate the eectiveness of our proposed stabilization strategy in this competitive context, we show the numerical simulations.