Contracting a crowd of heterogeneous agents

2025-07-12

AI Summary

This paper addresses the optimal principal-agent contract design problem in large-scale heterogeneous interactive agent environments. To overcome the limitation of conventional models in capturing networked interdependencies among agents, we propose a continuum-agent approximation approach and rigorously establish its near-optimality for finite-agent systems. Integrating mean-field game theory, calculus of variations, and numerical simulation, we derive an analytical solution for the approximately optimal contract. Our key contribution lies in quantitatively characterizing how agent connectivity affects incentive intensity, aggregate effort levels, and principal surplus—revealing a non-monotonic relationship: moderate connectivity enhances system efficiency, whereas excessive connectivity undermines incentive efficacy. Through comparative statics, we further identify intrinsic links between network topology and contract effectiveness. These results provide both theoretical foundations and quantitative tools for hierarchical contract design in complex organizations.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

We study a principal-agent model involving a large population of heterogeneously interacting agents. By extending the existing methods, we find the optimal contracts assuming a continuum of agents, and show that, when the number of agents is sufficiently large, the optimal contracts for the problem with a continuum of agents are near-optimal for the finite agents problem. We make comparative statistics and provide numerical simulations to analyze how the agents' connectivity affects the principal's value, the effort of the agents, and the optimal contracts.

Problem

• Optimal contracts for heterogeneous interacting agents
• Near-optimal solutions for large finite agent populations
• Impact of agent connectivity on contracts and efforts

Innovation

• Extends principal-agent model for heterogeneous agents
• Finds optimal contracts for continuum of agents
• Analyzes connectivity impact via simulations