Optimizing Contracts in Principal-Agent Team Production
Shiliang Zuo
TL;DR
The paper tackles a principal-agent team production problem with moral hazard where only aggregate output is observable, and contracts assign shares to agents. It introduces the induced production function $F(\\beta)=f(a(\\beta))$ and proves that, under an additive-separable condition $f(a)=h(\\sum_i g_i(a_i))$ with concave transformations, $F$ is quasiconcave. Exploiting this property, the authors reformulate the principal's nonconvex optimization into a family of convex or quasiconvex programs, including a production-constrained convex program and a share-constrained quasiconvex program, solvable by separation-oracle methods or projected-gradient techniques. They illustrate the approach with CES and Cobb-Douglas examples, deriving closed-form induced productions and simple optimal contracts in the CD case, thereby providing a computationally tractable path to optimal profit-sharing in team production.
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.