两轮择校中保持稳定性和时效性的机制
Stability-Preserving, Time-Efficient Mechanisms for School Choice in Two Rounds
摘要：
我们解决以下动态版本的学校选择问题：一个城市，名为城市，承认学生在两个时间上分开的轮，表示为$\mathcal{R}_1$和$\mathcal{R}_2$。在回合$\mathcal{R}_1$中，每个学校的容量是固定的，并且机制$\mathcal{M}_1$找到学生最优稳定匹配。在回合$\mathcal{R}_2$中，某些参数改变，例如，新的学生搬进城市或城市很乐意分配额外的座位给特定的学校。我们研究了一些这种设置，并给出了多项式时间算法，以获得一个稳定的匹配新的情况。众所周知，中途转学的学生，与她的同学不同步，可能会造成创伤性影响。这一事实将我们引导到两种类型的结果，第一种简单地不允许在回合$\mathcal{R}_2$中进行任何重新分配，第二种要求最小化重新分配次数的稳定匹配。对于后者，我们证明了最小化重新分配次数的稳定匹配形成稳定匹配格的子格。关于激励相容性的观察被编织到这些结果中。我们还给出了第三种类型的结果，即证明NP-硬度的机制，在一定的设置下，圆形$\mathcal{R}_2$。
英文摘要：
We address the following dynamic version of the school choice question: a city, named City, admits students in two temporally-separated rounds, denoted $\mathcal{R}_1$ and $\mathcal{R}_2$. In round $\mathcal{R}_1$, the capacity of each school is fixed and mechanism $\mathcal{M}_1$ finds a student optimal stable matching. In round $\mathcal{R}_2$, certain parameters change, e.g., new students move into the City or the City is happy to allocate extra seats to specific schools. We study a number of Settings of this kind and give polynomial time algorithms for obtaining a stable matching for the new situations. It is well established that switching the school of a student midway, unsynchronized with her classmates, can cause traumatic effects. This fact guides us to two types of results, the first simply disallows any re-allocations in round $\mathcal{R}_2$, and the second asks for a stable matching that minimizes the number of re-allocations. For the latter, we prove that the stable matchings which minimize the number of re-allocations form a sublattice of the lattice of stable matchings. Observations about incentive compatibility are woven into these results. We also give a third type of results, namely proofs of NP-hardness for a mechanism for round $\mathcal{R}_2$ under certain settings.
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。
