Econ Papers Daily / 期刊论文
固定人口匹配市场中重新稳定化的步数计算
Counting steps for re-stabilization in a matching market with fixed population
摘要
We study a one-to-one matching market where the population is fixed. If some exogenous reason disrupts a worker-firm pair in a stable matching, can equilibrium in the market be restored? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.
中文摘要
我们研究一个固定人口的一对一匹配市场。若某种外生原因破坏了稳定匹配中的一对工人-企业组合，市场均衡能否得以恢复？我们提出一种算法，将此情形建模为涉及空缺链的再稳定化过程。算法的每一步即为此链的一个环节。我们证明，该空缺链的长度与市场稳定匹配集合的格结构密切相关。具体而言，此长度可通过考虑由所涉及的初始和最终稳定匹配推导出的偏好中循环的基数来计算。