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, no truthful and deterministic mechanism can guarantee 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: BIC mechanisms can guarantee fairness notions that are unattainable by DSIC mechanisms 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. Notably, for the case of indivisible goods, we significantly strengthen the state-of-the-art negative result for efficient DSIC mechanisms, while also highlighting the limitations of BIC mechanisms, by showing that a very general class of welfare objectives is incompatible with Bayesian Incentive Compatibility. Combined these results give a near-complete picture of the power and limitations of BIC and DSIC mechanisms for the problem of allocating indivisible goods.

翻译：我们研究策略性代理人情形下的公平资源分配问题。众所周知，在该领域的多个基本问题中，诚实性与公平性不可兼得。例如，在分配不可分割物品时，即使对于具有可加估值函数的两个代理人，也不存在既能保证诚实性又能确定性地保证至多一项物品的无嫉妒性（EF1）的机制。同样，在蛋糕切割问题中，即使对于具有分段常值估值函数的两个代理人，也不存在总能输出成比例分配的诚实确定性机制。我们的研究源于如下观察：在公平分配语境中，诚实性通常被用作占优策略激励相容（DSIC）的同义词，其要求代理人无论其他代理人如何报告，都更偏好如实报告。本文转而聚焦于贝叶斯激励相容（BIC）机制，要求代理人在其他代理人报告的概率期望意义上，诚实报告能获得更优结果。我们证明：当代理人对彼此信息知之略少时，可达成结果将大为扩展——在不可分割物品分配与蛋糕切割这两个基本问题中，BIC机制能保障DSIC机制无法实现的公平性概念。我们进一步证明，即使代理人数量任意，只要代理人对彼此类型的先验信息满足中性条件，该结论依然成立。值得关注的是，针对不可分割物品情形，我们显著强化了当前最优的DSIC机制消极性结果，同时通过证明极广泛福利目标类别与贝叶斯激励相容不可兼得，揭示了BIC机制的局限性。这些结果共同为不可分割物品分配问题中BIC与DSIC机制的能力与局限性提供了近乎完整的图景。