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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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