复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同  

Optimal Contract for the Agency Problem Considering Agent’s Uncertain Effort in Reducing Project Duration

作　　者：马浚洋 黄晓霞[1] 傅颖诗 周晓光[1] MA Jun-yang;HUANG Xiao-xia;FU Ying-shi;ZHOU Xiao-guang(School of Economics and Management,University of Science and Technology Beijing,Beijing 100083,China;National University of Defense Technology,Changsha 410073,China;College of Management and Economics,Tianjin University,Tianjin 300072,China)

机构地区：[1]北京科技大学经济管理学院,北京100083 [2]国防科技大学文理学院,湖南长沙410073 [3]天津大学管理与经济学部,天津300072

出　　处：《中国管理科学》2021年第5期138-146,共9页Chinese Journal of Management Science

基　　金：国家社会科学基金资助项目(17BGL052);国家自然科学基金资助项目(71771023)。

摘　　要：本文着重研究复杂不确定环境下如何设计最优合同,以激励代理人减少项目持续期限。在代理问题中,以往的数量研究大多使用随机变量刻画项目参数和代理人的努力程度。但是,在某些情况下,项目参数和代理人的努力程度不能被历史数据获得,而必须由专家进行估计。运用不确定变量刻画专家对这些参数的估计,并且证明这样做是合理的。通过应用不确定理论,提出复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同模型。之后,为了解决这个问题,给出了该模型的确定性形式。此外,对是否考虑代理人不确定努力的最优合同进行了比较。结果显示,当其他条件相同时,委托人在考虑代理人不确定努力程度的合同中得到的期望收益不低于在没有考虑代理人不确定努力程度的合同中到的期望收益。最后,为了更好地展示模型的应用,给出了一个数值例子并进行了相关讨论。Agency problem occurs when the principal authorizes an agent for a specific project.In many industries,principal can earn higher return if the project is completed earlier.Since there is some asymmetric information between the two participators,principal cannot know how much effort that agent invests to accelerate completion of the project.The existence of asymmetric information may result in less agent’s effort which delays the expected project duration.This is because conflict exists between principal and agent and agent may act on his own interests instead of principal’s return.From principal’s perspective,he wishes that the agent will exert his effort to shorten the project duration to gain more profit.Besides,due to complexity of the market,in many cases project returns can hardly be predicted exactly by the principal in advance.This paper focuses on analyzing how to design an optimal contract for principal to stimulate the agent to expedite the project completion.Most previous researches used random variables to determine project parameters and the agent’s effort in project agency problems.However,in some cases,the project parameters and the agent’s effort cannot be obtained by the historical data and have to be estimated by experts.In this paper,uncertain variables are used to describe the experts’estimations of these parameters and the use of them is justified.By applying the uncertainty theory,an optimal contract for the agency problem considering the agent’s uncertain effort in reducing project duration is proposed.After that,the deterministic form of the model is given for solving the problem.Furthermore,the optimal contract considering the agent’s uncertain effort is compared with that without considering the agent’s uncertain effort.It is concluded that when everything else is same,the expected return of optimal contract is not less than that without considering the agent’s uncertain effort.Finally,an example is presented to illustrate the application of the proposed model.

关 键 词：代理问题 最优合同 不确定理论 代理人不确定努力程度 项目持续期限 

分 类 号：O224[理学—运筹学与控制论]