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Optimal Multi‐Agent Performance Measures For Team Contracts

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  • Hyeng Keun Koo
  • Gyoocheol Shim
  • Jaeyoung Sung

Abstract

We present a continuous‐time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sufficient statistic, and the other a nonsufficient statistic. As a consequence, the optimal aggregate performance measure in general is not a sufficient statistic, unless the principal is risk neutral. We further discuss agents' optimal effort choices using a “quadratic‐cost” example, which also strikingly suggests that team contracts sometimes provide lower‐powered effort incentives than individually separate contracts do.

Suggested Citation

  • Hyeng Keun Koo & Gyoocheol Shim & Jaeyoung Sung, 2008. "Optimal Multi‐Agent Performance Measures For Team Contracts," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 649-667, October.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:4:p:649-667
    DOI: 10.1111/j.1467-9965.2008.00352.x
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Collins, Alan R. & Maille, Peter, 2011. "Group decision-making theory and behavior under performance-based water quality payments," Ecological Economics, Elsevier, vol. 70(4), pages 806-812, February.
    2. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    3. Qi Luo & Romesh Saigal, 2020. "Dynamic Multiagent Incentive Contracts: Existence, Uniqueness, and Implementation," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    4. Barlo, Mehmet & Özdog˜an, Ayça, 2014. "Optimality of linearity with collusion and renegotiation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 46-52.
    5. Boualem Djehiche & Peter Helgesson, 2015. "The Principal-Agent Problem With Time Inconsistent Utility Functions," Papers 1503.05416, arXiv.org.
    6. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    7. Romuald Elie & Emma Hubert & Thibaut Mastrolia & Dylan Possamai, 2019. "Mean-field moral hazard for optimal energy demand response management," Papers 1902.10405, arXiv.org, revised Mar 2020.
    8. Yasuaki Wasa & Ken-Ichi Akao & Kenko Uchida, 2020. "Optimal Dynamic Incentive Contracts between a Principal and Multiple Agents in Controlled Markov Processes: A Constructive Approach," RIEEM Discussion Paper Series 2001, Research Institute for Environmental Economics and Management, Waseda University.
    9. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    10. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.

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