Game complexity of pricing and emission reduction in low-carbon supply chains with government regulation and fairness concerns under stagflation risk

Global climate and economic pressures necessitate low-carbon supply chain transitions, a process especially challenging for emerging markets and developing economies amid declining foreign investment and rising stagflation risks. This study uniquely integrates fairness concerns and stagflation risk into a nonlinear dynamical system, investigating a low-carbon supply chain consisting of a manufacturer and a capital-constrained retailer with fairness concerns. A dynamic Stackelberg game model is developed, incorporating government regulation on financing interest rates and fairness concerns. The principal findings are threefold. First, short-term analysis demonstrates the potential efficacy of government regulation within our model framework, showing that calibrated interventions via the financing rate ( δ ) and fairness concern adjustment coefficient (γ) can effectively guide the system toward a stable equilibrium under the specified parameter ranges. Second, long-term evolution reveals inherent instability: bounded rational strategy adjustments cause the system to cascade from period-doubling bifurcation into chaos once price adjustment speeds (v₁, v₂ ) exceed critical thresholds (e.g., v₁>0.239, v₂>0.3098 ), leading to severe performance deterioration. Third, the application of a time-delayed feedback control method shows promise in suppressing chaotic dynamics and restoring local stability within the simulated scenarios. These findings offer a novel theoretical lens for understanding supply chain instability and provide actionable insights for designing robust regulatory frameworks in volatile macroeconomic environments. Policymakers should manage price adjustment speeds and leverage synergistic carbon pricing and fairness regulations to mitigate instability and foster sustainable supply chain development.