Optimizing Contracts in Principal-Agent Team Production

TL;DR

This paper analyzes how a principal can design optimal profit-sharing contracts to incentivize a team of agents in a production setting where individual efforts are unobservable, using convex programming techniques for efficiency.

Contribution

It introduces a condition enabling the reformulation of the principal's optimization as convex programs, facilitating efficient computation of optimal contracts in team production models.

Findings

Optimal profit-sharing rules can be efficiently computed.

The principal's problem can be reformulated as convex programs under certain conditions.

The approach improves contract design in team production scenarios.

Abstract

We 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. We 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.