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The development of e-commerce and the green economy has prompted suppliers of green products to introduce internet channels by which products are directly sold to consumers. However, the emergence of "price wars" and "free riding" between the two channels after the introduction of online channels may affect the stability of the green supply chain. This paper uses optimization theory to investigate the impact of service spillover effects and different channel structures on the optimal decision of supply chain members in a Stackelberg game. By comparing the equilibrium outcomes of the single-channel and dual-channel supply chain in a setting with and without retail services, we observe that the supplier prefers to encroach on the market when services that retail locations provide largely spillover to and benefit the direct sales channel. Contrary to popular belief, a higher degree of service spillovers is beneficial for the retailer to achieve more returns under the dual-channel structure, whereas supplier encroachment will lead to a decline in the service level if the spillover degree is relatively low. In addition, the emission reduction level of products under supplier encroachment is always higher than that employed in the single-channel structure if consumers have both low-carbon preference and a high degree of service sensitivity. Finally, we expand our discussion by introducing the carbon cap-and-trade (CCT) mechanism to compare the conditions for achieving Pareto improvement under supplier encroachment. These results can provide helpful insights for decision-makers in supply chain management to implement effective channel selection and achieve sustainable development. [ABSTRACT FROM AUTHOR]