We study a multi-agent contracting problem where agents exert costly effort to achieve individually observable binary outcomes. While the principal can theoretically extract the full social welfare using a discriminatory contract that tailors payments to individual costs, such contracts may be perceived as unfair. In this work, we introduce and analyze anonymous contracts, where payments depend solely on the total number of successes, ensuring identical treatment of agents. We first establish that every anonymous contract admits a pure Nash equilibrium. However, because general anonymous contracts can suffer from multiple equilibria with unbounded gaps in principal utility, we identify uniform anonymous contracts as a desirable subclass. We prove that uniform anonymous contracts guarantee a unique equilibrium, thereby providing robust performance guarantees. In terms of efficiency, we prove that under limited liability, anonymous contracts cannot generally approximate the social welfare better than a factor logarithmic in the spread of agent success probabilities. We show that uniform contracts are sufficient to match this theoretical limit. Finally, we demonstrate that removing limited liability significantly boosts performance: anonymous contracts generally achieve an $O(\log n)$ approximation to the social welfare and, surprisingly, can extract the full welfare whenever agents' success probabilities are distinct. This reveals a structural reversal: widely spread probabilities are the hardest case under limited liability, whereas identical probabilities become the hardest case when limited liability is removed.

翻译：本文研究一个多智能体合约问题，其中智能体通过付出代价性努力以实现各自可观测的二元结果。理论上，委托人可以通过歧视性合约（即根据个体成本定制支付方案）提取全部社会福利，但此类合约可能被视为不公平。本工作引入并分析了匿名合约——其支付仅取决于成功总数，从而确保对所有智能体一视同仁。我们首先证明每个匿名合约都存在纯纳什均衡。然而，由于一般匿名合约可能存在多个均衡，且委托人效用的差距可能无界，我们将均匀匿名合约确定为一个理想的子类。我们证明均匀匿名合约能保证唯一均衡，从而提供稳健的性能保证。在效率方面，我们证明在有限责任条件下，匿名合约通常无法以优于智能体成功概率跨度对数因子的程度逼近社会福利，并证明均匀合约足以达到这一理论极限。最后，我们证明取消有限责任能显著提升性能：匿名合约通常可实现对社会福利的$O(\log n)$逼近，且令人惊讶的是，当智能体成功概率互不相同时，甚至能提取全部福利。这揭示了一种结构性反转：在有限责任下，广泛分布的概率是最困难的情形；而当有限责任被移除时，相同概率反而成为最困难的情形。