论文标题
分层随机匹配市场：等级与受欢迎程度成正比
Tiered Random Matching Markets: Rank is Proportional to Popularity
论文作者
论文摘要
我们研究了随机产生偏好的双面市场中稳定的婚姻问题。我们考虑各侧的代理，分为恒定数量的“软层”，这些层直观地表明了代理的质量。具体来说，一级代理商的公共得分都相同，并且每一侧的代理都有与另一方的公共分数成比例地生成的偏好。 我们计算了预期的平均等级，每个层中哪个代理在人类最佳稳定匹配中对其合作伙伴都有，并证明了渐近较大市场中平均等级的集中结果。此外，我们表明，尽管对等级产生了重大影响，但公共分数并没有强烈影响代理与另一端给定层的匹配的可能性。这概括了[Pittel 1989]的结果，该结果与均匀的偏好相对应。结果数量证明了由于代理商在市场上的异质吸引力而引起的竞争影响，我们对统一市场以外的等级进行了首次明确计算。
We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant number of "soft tiers", which intuitively indicate the quality of the agent. Specifically, every agent within a tier has the same public score, and agents on each side have preferences independently generated proportionally to the public scores of the other side. We compute the expected average rank which agents in each tier have for their partners in the men-optimal stable matching, and prove concentration results for the average rank in asymptotically large markets. Furthermore, we show that despite having a significant effect on ranks, public scores do not strongly influence the probability of an agent matching to a given tier of the other side. This generalizes results of [Pittel 1989] which correspond to uniform preferences. The results quantitatively demonstrate the effect of competition due to the heterogeneous attractiveness of agents in the market, and we give the first explicit calculations of rank beyond uniform markets.
