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

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.