Dynamic Incentive Design in Large Populations: A Mean Field Game Approach to the Principal-Agent Problem

We develop a continuous-time principal-agent model with mean-field interactions to study optimal incentive design in large economies. We extend Sannikov's recursive contracting framework to a setting where a single principal manages a continuum of heterogeneous agents whose behaviors are interdependent through aggregate effort externalities. Each agent's hidden efort affects their stochastic output, while the principal designs state-contingent contracts that must account for both individual moral hazard and collective behavior effects. The model generates a coupled system of forward-backward stochastic differential equations: a backward Hamilton-Jacobi-Bellman equation characterizing the principal's value function and optimal contracts, and a forward Fokker-Planck equation governing the evolution of the agent distribution. We establish conditions for mean-field equilibrium where the aggregate effort assumed by the principal when designing contracts coincides with the aggregate effort induced by agents following these contracts. Our numerical implementation reveals that despite complex state-dependent individual con tracts, the aggregate effort remains approximately stable over the contract horizon, while the distribution of continuation values exhibits increasing dis persion. Applications include compensation design in large frms, platform economies, and public incentive programs where individual actions generate aggregate externalities.