Study on Coordination Mechanism of <em>n</em>-Level Principal-Agent with Multi-Branches at the Chain Terminal Under Fairness Preferences

Based on the principal-agent theory, this paper constructs a n-level principal-agent model with multi-branches at the chain terminal, introduces the improved Fehr-Schmidt fairness preference theory, and establishes a n-level incentive framework covering the horizontal and vertical fairness preferences of terminal agents. By treating intermediate agents as a unified whole through the &quot;black-box&quot; approach, this paper focuses on analyzing the influence mechanism of terminal agents&#039; fairness preferences on effort level, incentive contract design and the operational efficiency of the entire principal-agent chain. The research results confirm that incorporating fairness preferences into the incentive mechanism design of green supply chain principal-agent relationships can effectively stimulate the production and operation enthusiasm of terminal agents, improve their effort levels; at the same time, it can significantly reduce agency costs in the principal-agent chain, optimize resource allocation efficiency, and thereby enhance green production efficiency. The conclusions and model design of this study provide a new theoretical path and practical reference for the collaborative operation and sustainable development of actual green supply chains with terminal multi-branch principal-agent structures.