Abstract: In the real world, an agent usually has a primary principal and a secondary principal at the same time, and there exist different principal-agent relationships between the primary principal, the secondary principal and the agent respectively. Drawing on the agent's utility function and effort cost function provided by Siqueira, Sandler and Cauley(2009), a principal-agent model is set under the condition of existing primary and secondary principals on the basis of traditional principal-agent theories and different roles of primary and secondary principals in the principal-agent relationship, and gets the optimal incentive compensation paid to the agent by the primary principal and the agent's optimal effort level for the primary principal is otiained, and the comparative analysis is carried on the principal-agent relationships under the condition of existing primary and secondary principals and that under the condition of a single principal based on the above-mentioned model. Then, taking MBA students, EMBA students, senior managers training students, MPAcc students, doctoral candidates, master degree candidates and undergraduates of our university as experimental subjects, experimental data is collected by interviews and questionnaire to make the experimental test of the model results. The main theoretical and experimental research results are as follows. Firstly, when the agent's effort for the secondary principal has externalities to the primary principal, the incentive compensation paid to the agent by the primary principal and the agent's optimal effort level for the primary principal will be higher than that under a single principal respectively. Secondly, when the agent's effort for the secondary principal has positive (or negative) externalities to the primary principal, the primary principal will gain more (or less) expected earning than that under a single principal. Thirdly, when the agent's effort for the secondary principal does not exist externalities to the primary principal, the incentive compensation paid to the agent by the primary principal, the primary principal's expected earning and the agent's optimal effort level for the primary principal will be same as that under a single principal respectively. Fourthly, the agent's total expected earning under the condition of existing primary and secondary principals will be higher than that under a single principal. The traditional principal-agent theory is expanded and deepened based on different roles of primary and secondary principals in the principal-agent relationship, and methodology is provided for solving the generally existing principal-agent problems between principals playing different roles and agents, and theoretical guidance for building the reasonable organizational system and governance mechanism, straightening out the internal principal-agent relationship between superiors and subordinates, improving the multiple principal-agent mechanism, and reducing the agent's moral hazard and the loss of primary principal.

Key words: primary and secondary principals, principal-agent model, externality