Dynamic competition and stability analysis of dual-track battery recycling systems under low-carbon transition

With the rapid development of the electric vehicle industry, the environmental pollution caused by retired batteries has made effective battery recycling increasingly important. The battery recycling market is characterized by the coexistence of whitelist-compliant enterprises and black-market workshops. To analyze their competitive relationship, this study develops a static Bertrand game and a discrete-time dynamic model under bounded rationality. The static analysis focuses on recycling prices, quantities, and research and development (R&D) effort, while the dynamic analysis examines how behavioral adjustment speeds and policy interventions jointly shape system stability. The results indicate that recycling R&D, consumer low-carbon preference, and regulatory pressure affect equilibrium decisions and profits, with some effects depending on technological and consumer characteristics. From a dynamic perspective, moderate adjustment speeds facilitate convergence, whereas excessive adjustments may induce oscillations and chaos. The stability threshold of each adjustment speed depends on the speeds of the other decision variables. Under the examined parameter settings, stronger regulatory pressure on black-market workshops expands the stability region, whereas higher subsidies for whitelist-compliant enterprises may shrink it. The joint policy analysis further shows that jointly increasing the three adjustment speeds reduces the range of subsidy-regulation combinations compatible with steady convergence. These findings provide insights into coordinating regulatory and subsidy policies while accounting for firms' adjustment behavior.