数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1749-1763.doi: 10.1007/s10473-021-0521-6

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A PENALTY FUNCTION METHOD FOR THE PRINCIPAL-AGENT PROBLEM WITH AN INFINITE NUMBER OF INCENTIVE-COMPATIBILITY CONSTRAINTS UNDER MORAL HAZARD

刘佳1, 王先甲1,2   

  1. 1. School of Economics and Management, Wuhan University, Wuhan 430072, China;
    2. Institute of Systems Engineering, Wuhan University, Wuhan 430072, China
  • 收稿日期:2019-09-05 修回日期:2021-04-14 出版日期:2021-10-25 发布日期:2021-10-21
  • 通讯作者: Jia LIU E-mail:liujia.06@163.com
  • 作者简介:Xianjia WANG,E-mail:wangxj@whu.edu.cn
  • 基金资助:
    This Research was supported by National Natural Science Foundation of China (72031009 and 71871171) and the National Social Science Foundation of China (20&ZD058).

A PENALTY FUNCTION METHOD FOR THE PRINCIPAL-AGENT PROBLEM WITH AN INFINITE NUMBER OF INCENTIVE-COMPATIBILITY CONSTRAINTS UNDER MORAL HAZARD

Jia LIU1, Xianjia WANG1,2   

  1. 1. School of Economics and Management, Wuhan University, Wuhan 430072, China;
    2. Institute of Systems Engineering, Wuhan University, Wuhan 430072, China
  • Received:2019-09-05 Revised:2021-04-14 Online:2021-10-25 Published:2021-10-21
  • Contact: Jia LIU E-mail:liujia.06@163.com
  • Supported by:
    This Research was supported by National Natural Science Foundation of China (72031009 and 71871171) and the National Social Science Foundation of China (20&ZD058).

摘要: In this paper, we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite, and where there are an infinite number of results that can be observed by the principal. This principal-agent problem has an infinite number of incentive-compatibility constraints, and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem. We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm. By analyzing the optimal solution obtained by the proposed penalty function method, we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.

关键词: principal-agent problem, mechanism design, moral hazard, semi-infinite programming problem, penalty function method

Abstract: In this paper, we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite, and where there are an infinite number of results that can be observed by the principal. This principal-agent problem has an infinite number of incentive-compatibility constraints, and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem. We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm. By analyzing the optimal solution obtained by the proposed penalty function method, we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.

Key words: principal-agent problem, mechanism design, moral hazard, semi-infinite programming problem, penalty function method

中图分类号: 

  • 91B44