Principal-Agent Problems Based on Credibility Measure

Principal-agent problems exist in all walks of social life, and agency theory is an essential approach to dealing with them under incomplete information. Due to incomplete information, it is necessary for the principal to design an optimal incentive scheme to induce the agent to choose the action which is the best possible for maximizing his own utility. In order to depict the incomplete information, the approach based on probability measure was provided in the literature. However, the Ellsberg paradox indicates that probability measure is not always appropriate to describe the vagueness and ambiguity in practical agency problems. Alternatively, this paper employs a fuzzy variable to characterize incomplete information in the agent's ability and applies a method based on credibility measure to deal with optimal contracting problems. With this in mind, a class of novel fuzzy agency models is developed. Under some particular assumptions, the sufficient and necessary conditions for optimal contracts are proven by the variational method, and the proposed work is supported with some numerical examples that illustrate the validity. Finally, three comparative results are presented to demonstrate the main innovations and the contributions to agency theory made by this work.