Skip to main content
Springer Nature Link
Log in

Optimal revenue-sharing contract based on forecasting effort for uncertain agency problem

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

This paper discusses an optimal contracting problem between a principal and an agent by establishing an uncertain agency model. Compared with the existing work, this research focuses on the risk cost caused by the wrong investment in a task based on an inaccurate assessment about the potential output. To avoid it, the principal authorizes the professional agent to make a more accurate assessment about the output in the light of his professional knowledge and experience, and then to show the principal the optimal amount invested in the task. Meanwhile, as an incentive for the agent to pay great forecasting effort to make the more accurate assessment about the output, the principal provides the agent with a revenue-sharing contract including a sharing ratio for him. On this view, this paper proposes the optimal revenue-sharing contract that provides guidance for the two participators to make their respective optimal decisions. Furthermore, the proposed work is supported with the numerical results by analyzing the evolutions of the optimal contract under various influencing factors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Ali MS (2014) Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays. Int J Mach Learn Cybern 5(1): 13–22

    Article  Google Scholar 

  2. Berle AA, Means CC (1932) The modern corporation and private property. Macmillan, New York

    Google Scholar 

  3. Cachon GP, Lariviere MA (2005) Supply chain coordination with revenue-sharing contracts: strengths and limitations. Manag Sci 51(1):30–44

    Article  MATH  Google Scholar 

  4. Cui LX, Zhao RQ, Tang WS (2007) Principal-agent problem in a fuzzy environment. IEEE Trans Fuzzy Syst 15(6):1230–1237

    Article  Google Scholar 

  5. De Kok AG, Graves SC (2003) Supply chain management: design, coordination and operation. North-Holland, Amsterdam

  6. Dubois D, Prade H (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum, New York

    Book  MATH  Google Scholar 

  7. Giannoccaro I, Pontrandolfo P (2004) Supply chain coordination by revenue sharing contracts. Int J Prod Econ 89(2):131–139

    Article  Google Scholar 

  8. Gilbert SM, Weng ZK (1998) Incentive effects favor non consolidating queues in a service system: the principal-agent perspective. Manag Sci 44(12):1662–1669

    Article  MATH  Google Scholar 

  9. Groves T (1973) Incentives in teams. Econometrica 41(4):617–631

    Article  MATH  MathSciNet  Google Scholar 

  10. Guesnerie R, Laffont JJ (1984) A complete solution to a classical of principal-agent problems with an application to the control on a self-managed firm. J Public Econ 25:329–369

    Article  Google Scholar 

  11. Holmstrom B (1979) Moral hazard and observability. Bell J Econ 10(1):74–91

    Article  Google Scholar 

  12. Jensen MC, Meckling WH (1976) Theory of the firm: managerial behavior, agency costs and ownership structure. J Fin Econ 3(4):305–360

    Article  Google Scholar 

  13. Kunter M (2012) Coordination via cost and revenue sharing in manufacturerCretailer channels. Eur J Oper Res 216(2):477–486

    Article  MATH  MathSciNet  Google Scholar 

  14. Laffont J, Martimort D (2002) The theory of incentives: the principal-agent model. Princeton University Press, Princeton

    Google Scholar 

  15. Lan YF, Du HB (2013) A warranty contract model with uncertain demands. Inform Int Interdisc J 16(2): 1037–1045

    Google Scholar 

  16. Lan YF, Liu YK, Sun GJ (2010) An approximation-based approach for fuzzy multi-period production planning problem with credibility objective. Appl Math Model 34(11):3203–3215

    Article  MathSciNet  Google Scholar 

  17. Lan YF, Zhao RQ, Tang WS (2011) A bilevel fuzzy principal-agent model for optimal nonlinear taxation probelms. Fuzzy Optim Decis Making 10(3):211–232

    Article  MATH  MathSciNet  Google Scholar 

  18. Lan YF, Zhao RQ, Tang WS (2011) Minimum risk criterion for uncertain production planning problems. Comput Ind Eng 61(3):591–599

    Article  MathSciNet  Google Scholar 

  19. Lan YF, Zhao RQ, Tang WS (2013) A yardstick competition approach to a multi-firm regulation problem under asymmetric information. J Comput Appl Math 249: 24–36

    Article  MATH  MathSciNet  Google Scholar 

  20. Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer-Verlag, Berlin

    Book  Google Scholar 

  21. Liu B (2013) Uncertainty theory, 4th ed.. http://orsc.edu.cn/liu/ut.pdf, Beijing

  22. Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450

    Article  Google Scholar 

  23. Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186

    Google Scholar 

  24. Mirrlees J (1974) Notes on welfare economics, information and uncertainty. North-Holland, Amsterdam

  25. Mirrlees J (1976) The optimal structure of authority and incentives within an organization. Bell J Econ 7(1):105–131

    Article  MathSciNet  Google Scholar 

  26. Nahmias S (1978) Fuzzy variables. Fuzzy Sets Syst 1(2):97–110

    Article  MATH  MathSciNet  Google Scholar 

  27. Palsule-Desai OD (2013) Supply chain coordination using revenue-dependent revenue sharing contracts. Omega 41(4):780–796

    Article  Google Scholar 

  28. Patrick B, Mathias D (2005) Contract theory. The Massachusetts Institute of Technology Press, London

    Google Scholar 

  29. Ross S (1973) The economic theory of agency: the principal’s problem. Am Econ Rev 63(2):134–139

    Google Scholar 

  30. Mu R, Lan YF, Tang WS (2013) An uncertain contract model for rural migrant worker’s employment problems. Fuzzy Optim Decis Making 12(1):29–39

    Article  MathSciNet  Google Scholar 

  31. She YH, He XL (2013) Uncertainty measures in rough algebra with applications to rough logic. Int J Mach Learn Cybern. doi: 10.1007/s13042-013-0206-0

    Google Scholar 

  32. Spence M, Zechhauser R (1971) Insurance, information and individual action. Am Econ Rev 61(2):380–387

    Google Scholar 

  33. Sun GJ, Liu YK, Lan YF (2010) Optimizing material procurement planning problem by two-stage fuzzy programming. Comput Ind Eng 58(1):97–107

    Article  Google Scholar 

  34. Wang GL, Tang WS, Zhao RQ (2013) An uncertain price discrimination model in labor market. Soft Comput 17(4):579–585

    Article  MATH  Google Scholar 

  35. Wang XS, Gao ZC, Guo HY (2012) Delphi method for estimating uncertainty distributions. Inform Int Interdisc J 15(2):449–459

    MathSciNet  Google Scholar 

  36. Wang XZ, Dong LC, Yan JH (2012) Maximum ambiguity based sample selection in fuzzy decision tree induction. IEEE Trans Knowl Data Eng 24(8): 1491–1505

    Article  Google Scholar 

  37. Wang XZ, He YL, Wang DD (2014) Non-naive bayesian classifiers for classification problems with continuous attributes. IEEE Trans Cybern 44(1): 21–39

    Article  Google Scholar 

  38. Wilson R (1969) The structure of incentive for decentralization under uncertainty. La Decision, Paris

    Google Scholar 

  39. Yao Z, Leungb S, Lai KK (2008) Manufacturer’s revenue-sharing contract and retail competition. Eur J Oper Res 186(2):637–651

    Article  MATH  Google Scholar 

  40. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgment

This work is partially supported by the National Natural Science Foundation of China under Grant No. 71271151 and No. 71301114, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20130032110015.

Author information

Authors and Affiliations

  1. Institute of Systems Engineering, Tianjin University, Tianjin, 300072, China

    Xiaoli Wu & Yanfei Lan

  2. College of Mathematics and Information Technology, Xingtai University, Xingtai, 054001, China

    Haitao Liu

Authors
  1. Xiaoli Wu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yanfei Lan
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Haitao Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yanfei Lan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, X., Lan, Y. & Liu, H. Optimal revenue-sharing contract based on forecasting effort for uncertain agency problem. Int. J. Mach. Learn. & Cyber. 5, 971–979 (2014). https://doi.org/10.1007/s13042-014-0243-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-014-0243-3

Keywords