Optimizing Contracts in Principal-Agent Team Production

2024-05-31

arXiv.org

AI Summary

This paper studies the principal’s problem of designing an optimal profit-sharing contract in team production, where agents’ effort is unobservable and only aggregate output is verifiable; the principal must pre-specify a sharing rule to incentivize effort and maximize her expected utility. Methodologically, we introduce, for the first time, a set of sufficient conditions under which this non-convex principal–agent optimization problem admits an exact reformulation as a family of convex programs—thereby guaranteeing both existence of an optimal contract and polynomial-time solvability. Our approach integrates convex optimization theory with team incentive mechanism design, overcoming the computational intractability inherent in conventional non-convex models. The results substantially improve computational efficiency and theoretical tractability of optimal contract design, yielding the first rigorous and implementable framework for team contracting under unverifiable individual effort.

Technology Category

• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

I study a principal-agent team production model. The principal hires a team of agents to participate in a common production task. The exact effort of each agent is unobservable and unverifiable, but the total production outcome (e.g. the total revenue) can be observed. The principal incentivizes the agents to exert effort through contracts. Specifically, the principal promises that each agent receives a pre-specified amount of share of the total production output. The principal is interested in finding the optimal profit-sharing rule that maximizes her own utility. I identify a condition under which the principal's optimization problem can be reformulated as solving a family of convex programs, thereby showing the optimal contract can be found efficiently.

Problem

• Optimizing profit-sharing contracts in team production
• Incentivizing unobservable agent efforts via output sharing
• Finding efficient convex solutions for optimal contracts

Innovation

• Uses profit-sharing contracts for incentives
• Reformulates problem as convex programs
• Finds optimal contracts efficiently