Dynamic Evolution Mechanism of Dual-Channel Supply Chain for Green Products Based on Equilibrium Price

With the growing emphasis on environmental sustainability and heightened market competition, the development and sale of green products have assumed a pivotal role in the operations of manufacturers. However, due to the constraints of bounded rationality within firms, the issue of dynamic pricing may rise. In light of this context, this paper employs a dual-channel framework to investigate the manufacturer’s green product development and pricing problem over a continuous timeframe. In this framework, the manufacturer markets traditional products through offline retailers while simultaneously launching green products via an online platform. In recognition of the practicality of multi-period operations, we also take online delay time lag, price adjustment speed, green input level, and consumer channel loyalty into account and explore their impacts on the equilibrium price of the dual-channel supply chain of green products. Utilizing the eigenvalue method, we delve into the dynamic pricing game and ascertain the existence of the unique Nash equilibrium point. Our research establishes critical thresholds for delay time lags and green inputs. Beyond these thresholds, equilibrium destabilizes, resulting in price unpredictability. Furthermore, we identify a crucial maximum for the rate at which manufacturers modify prices for green products in online markets. If this adjustment rate falls below the threshold, the system maintains stability. Additionally, both the extent of green inputs and the customer channel loyalty of manufacturers significantly impact both equilibrium stability and the resulting price within the system.