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 incentivize 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. We utilize this structure to design an FPTAS for additive success functions and a constant approximation algorithm for submodular success functions. Moreover, we show that adopting optimal fair contracts can lead to a 25% revenue increase compared to the optimal non-discriminatory contracts even for additive success functions.