Fair Team Contracts

Abstract

A principal selects a team of agents for collaborating on a joint project. The principal aims to design a revenue-optimal contract that incentivizes the team of agents to exert costly effort while satisfying fairness constraints. We show that the optimal fair contract ensures that there is a minimum share, and every agent receives a linear contract weakly higher than the minimum share that is sufficient to incentivize them to exert costly effort. Leveraging this structural characterization, we design an FPTAS for additive success functions and a constant approximation algorithm for submodular success functions. Moreover, we show that the optimal fair contract can outperform the non-discriminatory one by a factor $1.445$, and this bound is tight for both additive and submodular success functions.