标题： 关于概率分配规则 显示英文标题

标题： On Probabilistic Assignment Rules

摘要： 我们研究在概率框架下的具有初始禀赋的经典分配问题。 在此设定中，每个代理最初拥有一个物品，并对所有物品的整个集合有严格的偏好，目标是以一种满足诸如策略性诚实、帕累托效率和个体理性等理想性质的方式重新分配物品。 虽然Ma（1994）著名的结论表明，顶级交易循环（TTC）规则是唯一满足这些性质的确定性规则，但在概率领域类似的积极结果却很少。 我们在概率设定中扩展了Ma的结果，并考虑了SD效率、SD个体理性以及一种较弱的SD策略性诚实概念——SD顶级策略性诚实——它仅要求如果谎报能增加获得其最优先物品的概率，代理没有动机去谎报。 我们证明，在确定性禀赋下，一个概率规则是SD效率、SD个体理性和SD顶级策略性诚实的当且仅当它与TTC规则一致。 我们的结果在面对早期关于分数禀赋的不可能性结果（Athanassoglou和Sethuraman（2011））的情况下，突显了一个积极的可能性，并为在概率分配与禀赋之间调和理想性质提供了第一步。 显示英文摘要

摘要： We study the classical assignment problem with initial endowments in a probabilistic framework. In this setting, each agent initially owns an object and has strict preferences over the entire set of objects, and the goal is to reassign objects in a way that satisfies desirable properties such as strategy-proofness, Pareto efficiency, and individual rationality. While the celebrated result by Ma (1994) shows that the Top Trading Cycles (TTC) rule is the unique deterministic rule satisfying these properties, similar positive results are scarce in the probabilistic domain. We extend Ma's result in the probabilistic setting, and as desirable properties, consider SD-efficiency, SD-individual rationality, and a weaker notion of SD-strategy-proofness -- SD-top-strategy-proofness -- which only requires agents to have no incentive to misreport if doing so increases the probability of receiving their top-ranked object. We show that under deterministic endowments, a probabilistic rule is SD-efficient, SD-individually rational, and SD-top-strategy-proof if and only if it coincides with the TTC rule. Our result highlights a positive possibility in the face of earlier impossibility results for fractional endowments (Athanassoglou and Sethuraman (2011)) and provides a first step toward reconciling desirable properties in probabilistic assignments with endowments.