The Cost of Moral Hazard and Limited Liability in the Principal-Agent Problem

  • Felipe Balmaceda
  • Santiago R. Balseiro
  • Jose R. Correa
  • Nicolas E. Stier-Moses
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)

Abstract

In the classical principal-agent problem, a principal hires an agent to perform a task. The principal cares about the task’s output but has no control over it. The agent can perform the task at different effort intensities, and that choice affects the task’s output. To provide an incentive to the agent to work hard and since his effort intensity cannot be observed, the principal ties the agent’s compensation to the task’s output. If both the principal and the agent are risk-neutral and no further constraints are imposed, it is well-known that the outcome of the game maximizes social welfare. In this paper we quantify the potential social-welfare loss due to the existence of limited liability, which takes the form of a minimum wage constraint. To do so we rely on the worst-case welfare loss—commonly referred to as the Price of Anarchy—which quantifies the (in)efficiency of a system when its players act selfishly (i.e., they play a Nash equilibrium) versus choosing a socially-optimal solution. Our main result establishes that under the monotone likelihood-ratio property and limited liability constraints, the worst-case welfare loss in the principal-agent model is exactly equal to the number of efforts available.

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References

  1. 1.
    Alchian, A.A., Demsetz, H.: Production, information costs, and economic organization. American Economic Review 62(5), 777–795 (1972)Google Scholar
  2. 2.
    Babaioff, M., Feldman, M., Nisan, N.: Combinatorial agency. In: Proceedings of the 7th ACM Conference on Electronic Commerce (EC 2006), Ann Arbor, MI, pp. 18–28. ACM Press, New York (2006)CrossRefGoogle Scholar
  3. 3.
    Babaioff, M., Feldman, M., Nisan, N.: Free-riding and free-labor in combinatorial agency. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 109–121. Springer, Heidelberg (2009)Google Scholar
  4. 4.
    Grossman, S.J., Hart, O.D.: An analysis of the principal-agent problem. Econometrica 51(1), 7–45 (1983)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Holmström, B., Milgrom, P.: Multi-task principal-agent analyses: Incentive contracts, asset ownership and job design. Journal of Law, Economics and Organization 7, 24–52 (1991)Google Scholar
  6. 6.
    Holmström, B., Tirole, J.: Financial intermediation, loanable funds and growth. The Quarterly Journal of Economics 112(3), 663–691 (1997)CrossRefGoogle Scholar
  7. 7.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Jensen, M.C., Meckling, W.H.: Rights and production functions: An application to labor-managed firms and codetermination. The Journal of Business 52(4), 469–506 (1979)CrossRefGoogle Scholar
  9. 9.
    Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)MATHGoogle Scholar
  10. 10.
    Rothschild, M., Stiglitz, J.E.: Increasing risk: I. a definition. Journal of Economic Theory 2(3), 225–243 (1970)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Shapiro, C., Stiglitz, J.E.: Equilibrium unemployment as a worker discipline device. American Economic Review 74(3), 433–444 (1984)Google Scholar
  12. 12.
    Spence, M., Zeckhauser, R.: Insurance, information, and individual action. American Economic Review 61(2), 380–387 (1971)Google Scholar
  13. 13.
    Stiglitz, J.E.: Incentives and risk sharing in sharecropping. Review of Economic Studies 41(2), 219–255 (1974)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Felipe Balmaceda
    • 1
  • Santiago R. Balseiro
    • 2
  • Jose R. Correa
    • 1
  • Nicolas E. Stier-Moses
    • 2
  1. 1.Departamento de Ingeniería IndustrialUniversidad de ChileSantiagoChile
  2. 2.Graduate School of BusinessColumbia UniversityNew YorkUSA

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