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A Penalty Function Method for the Principal-Agent Problem with an Infinite Number of Incentive-Compatibility Constraints under Moral Hazard

Authors
  • Liu, Jia1
  • Wang, Xianjia1, 1
  • 1 Wuhan University, Wuhan, 430072, China , Wuhan (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 29, 2021
Volume
41
Issue
5
Pages
1749–1763
Identifiers
DOI: 10.1007/s10473-021-0521-6
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

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.

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