We study fair resource allocation with strategic agents. It is well-known that, across multiple fundamental problems in this domain, truthfulness and fairness are incompatible. For example, when allocating indivisible goods, there is no truthful and deterministic mechanism that guarantees envy-freeness up to one item (EF1), even for two agents with additive valuations. Or, in cake-cutting, no truthful and deterministic mechanism always outputs a proportional allocation, even for two agents with piecewise-constant valuations. Our work stems from the observation that, in the context of fair division, truthfulness is used as a synonym for Dominant Strategy Incentive Compatibility (DSIC), requiring that an agent prefers reporting the truth, no matter what other agents report. In this paper, we instead focus on Bayesian Incentive Compatible (BIC) mechanisms, requiring that agents are better off reporting the truth in expectation over other agents' reports. We prove that, when agents know a bit less about each other, a lot more is possible: using BIC mechanisms we can overcome the aforementioned barriers that DSIC mechanisms face in both the fundamental problems of allocation of indivisible goods and cake-cutting. We prove that this is the case even for an arbitrary number of agents, as long as the agents' priors about each others' types satisfy a neutrality condition. En route to our results on BIC mechanisms, we also strengthen the state of the art in terms of negative results for DSIC mechanisms.

翻译：我们研究存在策略性主体时的公平资源分配问题。众所周知，在该领域的多个基础问题中，真实性与公平性难以兼得。例如，在分配不可分割物品时，即使对于只有两个具有加性估值的主体，也不存在能够保证至多一项物品无嫉妒性（EF1）的、真实且确定性的机制。或者，在蛋糕切割问题中，即使对于只有两个具有分段常数估值的主体，也不存在总是能输出按比例分配结果的、真实且确定性的机制。我们的工作源于以下观察：在公平分配背景下，真实性被用作占优策略激励相容（DSIC）的同义词，要求无论其他主体报告何种信息，主体都更倾向于如实报告。在本文中，我们转而聚焦于贝叶斯激励相容（BIC）机制，该机制要求主体对其他主体报告类型的期望中如实报告能获得更好的结果。我们证明，当主体对彼此的了解稍少一些时，便能实现更多可能：通过BIC机制，我们能够在不可分割物品分配和蛋糕切割这两个基础问题中，克服上述DSIC机制面临的障碍。我们证明，即使对于任意数量的主体，只要主体关于彼此类型的先验满足中性条件，这一结论也成立。在得出关于BIC机制的结论过程中，我们还强化了关于DSIC机制负面结果的最新研究进展。