A Nash Bi-Level Optimization Framework for Competing Cleaner Closed-Loop Supply Chains in the Power Battery Industry

Background: Power battery closed-loop supply chains face simultaneous competition for scarce materials, subsidies, market demand, and recyclable batteries, while strategic decisions remain coupled with production, recovery, transport, inventory, and carbon-control operations. Methods: We develop a Nash-type bi-level framework for two homogeneous competing chains, in which simultaneous upper-level strategies determine conditional lower-level operating responses. Shared resources make feasibility strategy-dependent; therefore, the computational target is a finite-candidate approximate equilibrium rather than an analytically solved continuous equilibrium. Public-information-adapted benchmarks are used for finite-grid validation, algorithm and model comparison, and sensitivity analysis. Results: The proposed framework approaches the discretized reference equilibrium in the small-instance validation. In the stylized homogeneous-duopoly benchmark, the Nash-type structure provides a more suitable joint representation of competitive stability and implementation conditions than the selected Stackelberg and centralized-cooperative alternatives, while this result does not identify the competitive structure of the real battery industry. Sensitivity analysis provides directional, benchmark-specific evidence that demand and scarce-material supply are the clearest drivers, whereas policy, preference, and isolated technical parameters mainly reshape equilibrium allocation and structure. Conclusions: These findings support the framework as a conditional analytical tool for competing closed-loop supply chain planning.