Stability and Multistability in a Mixed Cournot Duopoly Game with Differentiated Products and Corporate Social Responsibility

This paper investigates the nonlinear dynamics of a discrete-time mixed Cournot duopoly consisting of a profit-maximizing firm and a Corporate Social Responsibility (CSR)-oriented firm under bounded rationality and product differentiation. The local stability of the Nash equilibrium is analyzed using the Jury stability criterion, while the global dynamics are explored through bifurcation diagrams, the largest Lyapunov exponent, phase portraits, critical curves, and basins of attraction. The analysis reveals rich nonlinear behaviors, including flip bifurcations, period-doubling cascades, limit cycles, chaotic attractors, and multistability arising from the coexistence of multiple attractors under identical parameter values. Basin structures demonstrate strong sensitivity to initial conditions, implying that different long-run market outcomes may emerge from the same economic environment. The numerical results further show that excessive adjustment speeds destabilize the market, whereas corporate social responsibility has a stabilizing effect by enlarging the stability region, delaying the onset of bifurcations, and reducing chaotic fluctuations. Moreover, the interaction between CSR and product differentiation plays a crucial role in shaping the long-run dynamics of the market. These findings provide new insights into the dynamic effects of socially responsible behavior in oligopoly markets and highlight CSR as an effective mechanism for enhancing market stability and mitigating complex nonlinear dynamics.