Research On Principal-Agent Problems Under Fuzzy Environments

This thesis gives a deep study of the principal-agent problem in a fuzzy environment. The groundwork is as follows:As in real principal-agent problems, the agents' characteristics are usually the agents' private information and can not be obtained by the principal easily, so the principal can only design the incentive mechanisms (contracts) by his subjective assessment on the agents' unknown characteristics. The subjective assessment is fuzzy by nature. As a result, in this thesis, the principal's subjective evaluations of the agents' imprecise characteristics are represented by fuzzy variables, and a fuzzy expected value model is formulated to maximize the principal's welfare.In solving the proposed model, the concept of credibility density and credibility distribution of fuzzy variable are adopted to convert the expected value model into an optimal control problem at first, then Pontryagin maximum principle is used to set up the Hamiltonian function and canonical system of differential equations as well as under the boundary condtions, and the specific solution procedures are given, and several numerical examples are presented to tesify the effectiveness of the proposed models by enumerating different utility functions of the principal. It is noticed from the optimal solutions that the best contract signed between the principal and the agents is usually a linear function and the problems formulated under similar situations can be solved by analytical methods.Finally, the proposed method is applied to a real supply chain problem.