Absorbing sets in roommate problems

We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other.     

Stochastic stability for roommate markets

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.     

析“从＋NP”格关系

汉语介词具有“赋格”的作用，介词“从”可以标记四种格关系：源点、行径、根由和时间。运用“格”语法理论对“从＋NP”格关系进行分析，旨在对介词“从”语义功能的研究以及对外汉语教学起到一定的积极作用。