防策略且浪费最少的随机分配
Strategy-Proof and Minimally Wasteful Random Assignment
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中文总结 AI 辅助
该研究针对不可分物品的随机分配问题，证明满足特定条件的机制必然存在至少1/6的代理人-物品浪费，且随机串行独裁（RSD）在相关场景中达到浪费最小界限，随机延期接受（RDA）浪费更低但违反平等对待条件。
中文摘要 AI 辅助
我们研究在具有严格偏好和外部选择的一组代理人之间对不可分物品进行随机分配的问题。当代理人可能将某些物品评为不可接受时，我们从事前视角考虑不同的物品浪费衡量概念。最自然的是q-代理人-物品浪费，即至少有概率q使得某一代理人及其一个可接受物品均未被分配。一方面，我们证明，任何满足几乎平等者平等对待（指对物品具有相同排序的任意两个代理人，在他们均认为可接受的物品上获得相同的概率份额）、防策略性和事后弱非浪费性（指在支撑集的任何分配中，都不能出现某一代理人及其一个可接受物品均未被分配的情况）的机制，必然是q-代理人-物品浪费的，其中q≥1/6。另一方面，我们证明，对于四个代理人或三个物品，随机串行独裁（RSD）在该类机制中达到1/6的最小界限。此外，我们考虑q-物品浪费，即某一物品以概率q未被分配，而认为该物品可接受的代理人总体以概率q未被分配。我们再次证明，对于三个物品，RSD在该类机制中关于q-物品浪费达到1/4的最小界限。最后，我们证明，随机延期接受（RDA）可能比RSD的代理人-物品浪费程度严格更低（但代价是违反几乎平等者平等对待）。
英文摘要
We study random assignment of indivisible objects among a set of agents with strict preferences and outside options. When agents may rank some objects as unacceptable, we consider different notions of measuring waste of object(s) from an ex-ante perspective. The most natural one is $q$-agent-object-waste whereby both one agent and one of his acceptable objects are unassigned with at least probability $q$. On the one hand, we show that any mechanism satisfying equal treatement of almost equals (whereby any two agents with identical rankings over objects receive the same probability shares for objects they both regard acceptable), strategy-proofness and ex-post weak non-wastefulness (whereby in any assignment in the support we cannot have that both one agent and one of his acceptable objects are unassigned) must be $q$-agent-object-wasteful with $q\geq \frac{1}{6}$. On the other hand, we show that random serial dictatorship (RSD) attains the minimal bound of $\frac{1}{6}$ in this class for four agents or three objects. In addition, we consider $q$-object-wastefulness where an object remains unassigned with probability $q$, while agents, who consider it acceptable, remain unassigned with aggregate probability $q$. We again show that RSD attains the minimal bound of $\frac{1}{4}$ in this class of mechanisms with respect to $q$-object-wastefulness for three objects. Finally, we show that random deferred acceptance (RDA) may be strictly less agent-object-wasteful than RSD (but at the cost of violating equal treatment of almost equals).
