无差异随机分配中效率与策略防误的不相容性
Incompatibility of Efficiency and Strategyproofness in the Random Assignment Setting with Indifferences
摘要：
一个基本的资源分配设置是随机分配问题，其中代理表达对象的偏好，然后随机分配给代理。2001年，Bogomolnaia和Moulin提出了概率序列（PS）机制，该机制是一种匿名的，中立的，Pareto最优的，弱防策略的机制，当偏好被认为是相对于随机优势。当代理人对单个对象有严格的偏好时，结果成立。当主体之间存在无差异时，是否存在满足相同性质的机制一直是一个悬而未决的问题。我们发现，对于这个更一般的域，不存在扩展的PS是事后有效的和弱strategyproof。结果令人惊讶，因为它甚至不需要额外的对称或公平条件，如匿名，中立或平等对待平等。我们的结果进一步证明了Katta和Sethuraman（2006）的扩展PS机制缺乏弱SD-防策略性不是扩展PS的设计缺陷，而是由于PS在全偏好域中的效率和防策略性的内在不相容性。
英文摘要：
A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial (PS) mechanism that is an anonymous, neutral, Pareto optimal, and weak strategyproof mechanism when the preferences are considered with respect to stochastic dominance. The result holds when agents have strict preferences over individual objects. It has been an open problem whether there exists a mechanism that satisfies the same properties when agents may have indifference among the objects. We show that for this more general domain, there exists no extension of PS that is ex post efficient and weak strategyproof. The result is surprising because it does not even require additional symmetry or fairness conditions such as anonymity, neutrality, or equal treatment of equals. Our result further demonstrates that the lack of weak SD-strategyproofness of the extended PS mechanism of Katta and Sethuraman (2006) is not a design flaw of extended PS but is due to an inherent incompatibility of efficiency and strategyproofness of PS in the full preference domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
