Dynamic Mean Field Contracting: Relative Performance Evaluation, Tournaments, and Incentives under Competition

Heng-Fu Zou ()

No 791, CEMA Working Papers from China Economics and Management Academy, Central University of Finance and Economics

Abstract: This paper develops a dynamic theory of contracting with one principal and many agents, extending the promised-utility framework of Sannikov (2008) to environments with competition, correlated outputs, and relative performance evaluation (RPE). We show that the first-order approach remains valid when the principal filters performance through generalized least squares (GLS) residuals of peer outputs, which minimize variance while preserving incentive slopes. The principal's Hamilton- Jacobi-Bellman equation links optimal effort to three forces: marginal revenue, signal informativeness, and intertemporal insurance. In a linear-quadratic environment, equilibrium effort is uniquely determined by a contraction mapping, resolving the multiplicity of equilibria found in static models such as Mookherjee (1984). We further unify Lazear-Rosen (1981) tournaments and linear RPE contracts as diffusion-driven special cases - Gaussian, CIR, and lognormal - within a mean field game system. The framework rationalizes empirical puzzles in executive pay, sales contests, and financial benchmarking, and generates new testable predictions about incentives and organizational scale.

Keywords: Dynamic contracts; Principal-agent problem; Multi-agent incentives; Relative performance evaluation; Tournaments; Mean field games; Hamilton-Jacobi-Bellman equation; Fokker-Planck dynamics; Incentives and insurance; Executive compensation; Organizational design (search for similar items in EconPapers)
Pages: 23 pages
Date: 2025-09-19
New Economics Papers: this item is included in nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:cuf:wpaper:791

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