Satisfy The Mirrlees-rogerson, Sufficient Conditions For Two Types Of Distribution Functions

The research purpose of principal-agent problem is to devise the incentive contracts for asymmetric information game problem. The mathematical model of the principal-agent problem is a bi-level programming. In the economic field, the first-order approach is a technical shortcut widely used to solve this problem. However, the application scope of the first order approach is very limited. The best known set of sufficient conditions for its validity is due to Mirrlees and Rogerson and requires that the distribution function is convex in effort and has a likelihood ratio increasing in output. On the other hand, multi-task principal-agent can be widely applied lots of practical problem, which got rich attention from academic field recently.The main contribution of this paper lies in two aspects:First, this paper provides two rich families of examples displaying both properties CDFC and MLRP. Then, it discusses the density functions' characteristic by three concrete examples. From the discussion we can conclude that: Mirrlees-Rogerson conditions do not regulate the shape of the density function, unimodal, bimodal or monotone density functions all can satisfy Mirrlees-Rogerson conditions. Our research enlarges the first order approach's application scope.Second, this paper uses Holmstrom-Milgrom model to solve the incentive contracts devising problem for external auditing. Holmstrom and Milgrom prove the existence of this model's solution from economic aspect. This paper proves the existence of the solution from operations research aspect. Then, this paper gives the economic explanation for the solution and gets some meaningful conclusion for decision making.