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.

翻译：委托方为一项联合项目选择一组代理进行协作。委托方旨在设计一种收益最优的契约，在满足公平性约束的同时，激励代理团队付出高成本的努力。我们证明，最优公平契约确保存在一个最低份额，且每位代理获得的线性契约均不低于足以激励其付出高成本努力的最低份额。利用这一结构，我们针对加性成功函数设计了一种完全多项式时间近似方案（FPTAS），并针对子模成功函数设计了一种常数近似算法。此外，我们表明，即使对于加性成功函数，采用最优公平契约相比最优非歧视性契约可带来高达25%的收益提升。