Contracting a crowd of heterogeneous agents

TL;DR

This paper develops explicit optimal contracts for large, heterogeneous agent populations with network spillovers, providing scalable approximations and insights into incentive targeting based on network position.

Contribution

It introduces a linear-quadratic framework for finite and continuum agent models, deriving explicit contracts and analyzing their stability and effectiveness.

Findings

Continuum contracts approximate finite-agent solutions with error of order 1/N.

Optimal incentives are targeted toward agents with larger spillovers.

Numerical examples illustrate how network position influences effort and principal's value.

Abstract

We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadratic framework, we solve the finite-agent problem and its continuum limit, obtaining explicit optimal contracts and equilibrium efforts. We show that the continuum contract can be evaluated on a large finite sample of agents to obtain admissible contracts that achieve the finite-agent principal's value up to an error of order 1/N. This provides a scalable approximation for settings with many interacting agents. We also prove stability with respect to perturbations of the interaction function and provide comparative statics and numerical examples showing how network position affects effort, incentives, and the principal's value. The results identify how optimal incentives should be targeted toward agents whose actions generate larger spillovers.