Acta mathematica scientia,Series B ›› 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

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).

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

CLC Number: 

  • 91B44
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