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

doi:10.1007/s10473-021-0521-6

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 WANG^1,2

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

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

Jia LIU, Xianjia WANG. A PENALTY FUNCTION METHOD FOR THE PRINCIPAL-AGENT PROBLEM WITH AN INFINITE NUMBER OF INCENTIVE-COMPATIBILITY CONSTRAINTS UNDER MORAL HAZARD[J].Acta mathematica scientia,Series B, 2021, 41(5): 1749-1763.

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References

[1] Philippon T, Skreta V. Optimal interventions in markets with adverse selection. American Economic Review, 2012, 102(1):1-28
[2] Oh S, Özer O. Mechanism design for capacity planning under dynamic evolutions of asymmetric demand forecasts. Management Science, 2013, 59(4):987-1007
[3] Hoppe E, Schmitz P W. Do sellers offer menus of contracts to separate buyer types? an experimental test of adverse selection theory. Games and Economic Behavior, 2015, 89:17-33
[4] Fuchs W, Skrzypacz A. Government interventions in a dynamic market with adverse selection. Journal of Economic Theory, 2015, 158:371-406
[5] Balkenborg D, Makris M. An undominated mechanism for a class of informed principal problems with common values. Journal of Economic Theory, 2015, 157:918-958
[6] Diasakos T M, Koufopoulos K. (Neutrally) Optimal mechanism under adverse selection:The canonical insurance problem. Games and Economic Behavior, 2018, 111:159-186
[7] Citanna A, Siconolfi P. Designing insurance markets with moral hazard and nonexclusive contracts. Economic Theory, 2016, 62:325-360
[8] Piskorski T, Westerfield M M. Optimal dynamic contracts with moral hazard and costly monitoring. Journal of Economic Theory, 2016, 166:242-281
[9] Hong S, Wernz C, Stillinger J D. Optimizing maintenance service contracts through mechanism design theory. Applied Mathematical Modelling, 2016, 40(21/22):8849-8861
[10] Strausz R. A theory of crowdfunding:A mechanism design approach with demand uncertainty and moral hazard. American Economic Review, 2017, 107(6):1430-1476
[11] Holmström B. Moral hazard and observability. Bell Journal of Economics, 1979, 10(1):74-91
[12] Laffont J J, Martimort D. The Theory of Incentives:The Principal-Agent Model. Princeton, New Jersey:Princeton University Press, 2002
[13] Mirrlees J A. The theory of moral hazard and unobservable behaviour:Part I. Review of Economic Studies, 1999, 66(1):3-21
[14] López M, Still G. Semi-infinite programming. European Journal of Operational Research, 2007, 180(2):491-518
[15] Jess A, Jongen H T, Nerali L, et al. A semi-infinite programming model in data envelopment analysis. Optimization, 2001, 49(4):369-385
[16] Vaz A I F, Fernandes E M G P, Gomes M P S F. Robot trajectory planning with semi-infinite programming. European Journal of Operational Research, 2004, 153(3):607-617
[17] Vzquez F G, Rückmann J J. Semi-infinite programming:properties and applications to economics//New Tools of Economic Dynamics. Berlin, Heidelberg:Springer, 2005
[18] Reemtsen R. Discretization methods for the solution of semi-infinite programming problems. Journal of Optimization Theory and Applications, 1991, 71(1):85-103
[19] Wan Z P, Wang X J, He J L, et al. Asymptotic approximation method and its convergence on semi-infinite programming. Acta Mathematica Scientia, 2006, 26B(1):17-24
[20] Liu G X. A homotopy interior point method for semi-infinite programming problems. Journal of Global Optimization, 2007, 37(4):631-646
[21] Still G. Generalized semi-infinite programming:numerical aspects. Optimization, 2001, 49(3):223-242
[22] Qi L, Wu S Y, Zhou G. Semismooth newton methods for solving semi-infinite programming problems. Journal of Global Optimization, 2003, 27(2/3):215-232
[23] Tanaka Y. A trust region method for semi-infinite programming problems. International Journal of Systems Science, 1999, 30(2):199-204
[24] Rückmann J J, Shapiro A. Augmented lagrangians in semi-infinite programming. Mathematical Programming, 2009, 116(2):499-512
[25] Lin Q, Loxton R, Teo K L, et al. A new exact penalty method for semi-infinite programming problems. Journal of Computational and Applied Mathematics, 2014, 261(4):271-286
[26] Okuno T, Fukushima M. An interior point sequential quadratic programming-type method for logdeterminant semi-infinite programs. Journal of Computational and Applied Mathematics, 2020, 316(1):112784
[27] Marendet A, Goldsztejn A, Chabert G, et al. A standard branch-and-bound approach for nonlinear semiinfinite problems. European Journal of Operational Research, 2020, 282(2):438-452

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

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