贝叶斯公平分配：具有相关估值的选取序列中的真实性
Bayesian Fair Division: Truthfulness in Picking Sequence with Correlated Valuations
AI总结：
本文针对两智能体的贝叶斯公平分配模型，证明估值正相关时序列分配机制的讲真话构成贝叶斯纳什均衡，但该真实性无法扩展到多智能体场景，揭示了序列机制真实性的根本局限。
AI中文摘要：
序列分配机制是不可分割物品公平分配中被广泛研究的一类机制（例如循环赛制），其中智能体按预设的选取顺序轮流选取物品。已知序列分配机制不具有真实性：当某个智能体最偏好的物品未被其他智能体估值时，该智能体可能会通过操纵机制，选择推迟选取该物品，转而竞争其他被其他智能体估值的、偏好稍低的物品。两个根本原因是每个智能体对其他智能体的估值具有完全知识，且每个物品对每个智能体的价值可能存在显著差异。当每个智能体仅拥有关于其他智能体估值的部分信息，且这些估值大致一致时，机制是否会更具真实性？这自然推动了贝叶斯公平分配模型的研究。在本文中，我们针对两个智能体的情况肯定地回答了该问题。在贝叶斯模型下，我们精确刻画了促使智能体讲真话的“大致一致性”的程度。特别地，我们表明对于两个智能体的情况，当估值正相关时，在序列分配机制下讲真话构成贝叶斯纳什均衡。然而，我们表明真实性无法扩展到两个以上智能体的情况。对于两个以上智能体，我们揭示了一种不同于上述推迟选取高价值但竞争力较低物品的新型操纵。我们的结果揭示了序列机制真实性的一个根本局限。
英文摘要：
Sequential allocation mechanisms contain a class of widely studied mechanisms (e.g., round-robin) in the fair division of indivisible goods, where agents take turns picking items in a predefined picking order. It is known that the sequential allocation mechanisms are not truthful: when an agent's most preferred item is not valued by others, the agent may manipulate the mechanism by choosing to defer picking that item and instead competing for another slightly less preferred item that is valued by others. Two underlying reasons are that each agent has perfect knowledge of the others' valuations, and each item's value to each agent can differ significantly. Will the mechanism be more truthful when each agent only has partial information about the others' valuations, which are known to be roughly consistent? This naturally motivates the study of the Bayesian fair division model. In this paper, we answer this question affirmatively for two agents. Under the Bayesian model, we precisely characterize the extent of this ``rough consistency'' that incentivizes agents' truth-telling. In particular, we show that for the case of two agents, when the valuations are positively correlated, truth-telling forms a Bayesian Nash equilibrium under the sequential allocation mechanisms. However, we show that truthfulness fails to extend to the setting with more than two agents. For more than two agents, we reveal a new type of manipulation that is different from the above-mentioned manipulation that defers a highly valued but less competitive item. Our result reveals a fundamental limitation on the truthfulness of sequential mechanisms.
