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Mean-Field Principal-Agent Contracts with Relative Performance: An Explicit Formula under Sannikov-Style Primitives

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  • Heng-fu Zou

Abstract

We analyze a continuum of risk-neutral agents working under a risk-neutral principal. Each agent's output depends on hidden effort and random shocks, while the principal observes both individual outcomes and their cross-sectional average. Agents value consumption linearly but face quadratic effort costs, with all parties discounting at a common rate. We derive the optimal contract in closed form. It consists of a fixed salary plus a relative-performance component that rewards an agent's outcome compared to the group average. This design preserves incentives, since no individual can influence the average, while filtering out common risks and transitory fluctuations. In the unique symmetric equilibrium, all agents exert constant efficient effort, and the fixed salary adjusts to ensure participation. Because of risk neutrality, the contract is independent of the level of randomness.

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  • Heng-fu Zou, 2025. "Mean-Field Principal-Agent Contracts with Relative Performance: An Explicit Formula under Sannikov-Style Primitives," CEMA Working Papers 789, China Economics and Management Academy, Central University of Finance and Economics.
    • Handle: RePEc:cuf:wpaper:789
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    References listed on IDEAS

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    1. Villeneuve, Stéphane & Biais, Bruno & Gersbach, Hans & Rochet, Jean-Charles & von Thadden, Ernst-Ludwig, 2024. "Dynamic Contracting with Many Agents," TSE Working Papers 24-1511, Toulouse School of Economics (TSE).
    2. Andrei Shleifer, 1985. "A Theory of Yardstick Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(3), pages 319-327, Autumn.
    3. René Carmona & Peiqi Wang, 2021. "Finite-State Contract Theory with a Principal and a Field of Agents," Management Science, INFORMS, vol. 67(8), pages 4725-4741, August.
    4. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    5. 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.
    6. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
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