Optimal Contract Design Of Agents With Heterogeneous Capabilities

The limited rationality of the real person and the existence of the transaction cost of the agreement result in the incompleteness of the complete contract.A large number of scholars have paid more attention to the frequent occurrence and widespread use of the incomplete characteristics of contracts in the real economy.They focus on the incomplete characteristics of contracts and put forward practical problems and countermeasures under various scenarios.The incomplete contract theory thus formed has also become a basic theoretical tool in the fields of corporate development strategy,investment and financing,personnel management,etc.It has become a realistic and objective need in the economic field to master and reasonably use the incomplete contract theory.In addition,at the level of real economic life,the moral hazard and adverse selection of heterogeneous agents often appear separately or simultaneously,making the real contract problem more complicated.In this paper,based on the similar situation,the optimal contract setting problem is modeled.The limited rationality of the real person and the existence of the transaction cost of the agreement result in the incompleteness of the complete contract.A large number of scholars have paid more attention to the frequent occurrence and widespread use of the incomplete characteristics of contracts in the real economy.They focus on the incomplete characteristics of contracts and put forward practical problems and countermeasures under various scenarios.The incomplete contract theory thus formed has also become a basic theoretical tool in the fields of corporate development strategy,investment and financing,personnel management,etc.It has become a realistic and objective need in the economic field to master and reasonably use the incomplete contract theory.In addition,at the level of real economic life,the moral hazard and adverse selection of heterogeneous agents often appear separately or simultaneously,making the real contract problem more complicated.In this paper,based on the similar situation,the optimal contract setting problem is modeled.This paper studies the effect of agent heterogeneity on the optimal static contract design in discontinuous time.The optimal solution of the same type agent contract and the explicit solution of the type agent separation equilibrium contract are solved.It is found that the expected utility of the principal is improved compared with the type agent separation equilibrium contract and the type agent same contract.Under the same type of agent contract,the high-capacity agent will choose to imitate the low-capacity agent in order to obtain camouflage benefits.Under the type agent separation equilibrium contract,the high ability agent does not choose to imitate the low ability agent to choose the contract contract,but only chooses the contract with higher incentive degree.The influence of agent heterogeneity on the optimal dynamic contract is further studied.The agent continuation value equation and the principal utility dynamic equation are established,and the expressions of the optimal payment and the optimal effort are obtained.Later,the inverse selection behavior will be added to the model.Consider the adverse selection strategies of agents with different capabilities.The expressions of the optimal payment and the optimal effort obtained by the agent under the adverse selection are obtained.Through numerical analysis of the results,it is found that when the retention effect is large,the client provides a screening contract rather than a termination contract.If the retention effect is small,only selecting high-capacity agents will incur more costs,and the project implementation is insufficient.The following two contract modeling processes and results are discussed.The applicability of the two types of models is expounded from the long-term and short-term perspectives.In the short term,the static contract model is more in line with the contract setting in real life;In the long run,the dynamic contract model is more suitable for adjusting the contract setting of project arrangement over time.