Uncertain agency models with multi-dimensional incomplete information based on confidence level

This paper discusses a principal-agent problem with multi-dimensional incomplete information between a principal and an agent. Firstly, how to describe the incomplete information in such agency problem is a challenging issue. This paper characterizes the incomplete information by uncertain variable, because it has been an appropriate tool to depict subjective assessment and model human uncertainty. Secondly, the relevant literature often used expected-utility-maximization to measure the two participators' goals. However, Ellsberg paradox indicates that expected utility criterion is not always appropriate to be regarded as decision rule. For this reason, this paper presents another decision rule based on confidence level. Instead of expected-utility-maximization, the principal's aim is to maximize his potential income under the acceptable confidence level, and the agent's aim depends on whether he has private information about his efforts. According to the agent's different decision rules, three classes of uncertain agency (UA) models and their respective optimal contracts are presented. Finally, a portfolio selection problem is studied to demonstrate the modeling idea and the viability of the proposed UA models.