Optimal pricing and complex analysis for green e-commerce platform supply chains

A computational dynamic game framework is proposed to analyze the nonlinear interplay between pricing strategies and green investments in dual-channel e-commerce supply chains (EPSCs). By integrating static equilibrium analysis with nonlinear system dynamics, three major contributions are established. First, through a static game model, key thresholds for switching between decentralized and centralized decision-making mechanisms are identified. Centralized decision-making optimizes supply chain profitability under high green investment costs, as it internalizes cross-channel externalities. However, the decentralized mechanism becomes more advantageous under low green investment costs with minimal commission rates, reducing double marginalization losses. Second, employing bifurcation diagrams and Lyapunov exponent analysis, the relationship between adjustment speeds and system stability is revealed. Decentralized systems exhibit wider stability regions than centralized ones due to manufacturers' first-mover advantage. Beyond critical thresholds, chaotic states emerge, disrupting profit predictability. Third, an adaptive control mechanism is proposed to stabilize chaotic pricing oscillations. These findings equip platforms with computational tools to dynamically calibrate pricing-green investment trade-offs, while policymakers can leverage cost thresholds to design green subsidy schemes. The framework bridges game theory and nonlinear dynamics, offering a paradigm for sustainable e-commerce operations under bounded rationality.