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Combinatorial agency


  • Babaioff, Moshe
  • Feldman, Michal
  • Nisan, Noam
  • Winter, Eyal


We study a combinatorial variant of the classical principal-agent model. In our setting a principal wishes to incentivize a team of strategic agents to exert costly effort on his behalf. Agentsʼ actions are hidden and the principal observes only the outcome of the team, which depends stochastically on the complex combinations of the efforts by the agents. The principal seeks the mechanism that maximizes the principalʼs net revenue given an equilibrium behavior of the agents. We investigate the structure of the optimal mechanism for various production technologies as the principalʼs value from the project varies. In doing so we quantify the gap between the first-best and second-best solutions. Our results highlight the qualitative and quantitative differences between production technologies that exhibit complementarities and substitutabilities between the agentsʼ actions. In comparing the first best with the second best we highlight the role of effort monitoring by the principal. As we shall see, the benefit from monitoring crucially depends on the underlying technology, with the two polar cases being perfect substitution and perfect complementarity.

Suggested Citation

  • Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:999-1034 DOI: 10.1016/j.jet.2012.01.010

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    References listed on IDEAS

    1. Eyal Winter, 2004. "Incentives and Discrimination," American Economic Review, American Economic Association, vol. 94(3), pages 764-773, June.
    2. Strausz, Roland, 1999. "Efficiency in Sequential Partnerships," Journal of Economic Theory, Elsevier, vol. 85(1), pages 140-156, March.
    3. Yeon-Koo Che & Seung-Weon Yoo, 2001. "Optimal Incentives for Teams," American Economic Review, American Economic Association, vol. 91(3), pages 525-541, June.
    4. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    5. Ilya Segal, 1999. "Contracting with Externalities," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 337-388.
    6. Segal, Ilya, 2003. "Coordination and discrimination in contracting with externalities: divide and conquer?," Journal of Economic Theory, Elsevier, vol. 113(2), pages 147-181, December.
    7. Eyal Winter, 2010. "Transparency and incentives among peers," RAND Journal of Economics, RAND Corporation, vol. 41(3), pages 504-523.
    8. Smorodinsky, Rann & Tennenholtz, Moshe, 2006. "Overcoming free riding in multi-party computations--The anonymous case," Games and Economic Behavior, Elsevier, vol. 55(2), pages 385-406, May.
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    More about this item


    Agency theory; Incentives; Contracts; Hidden-action; Moral hazard;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law


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