分层随机匹配市场：排名与受欢迎程度成正比
Tiered Random Matching Markets: Rank is Proportional to Popularity
摘要：
本文研究了具有随机偏好的双边市场中的稳定婚姻问题。我们认为代理商在每一方分为一个恒定数量的“软层”，直观地表明代理商的质量。具体来说，一个层内的每个代理都有相同的公共分数，每一方的代理都有与另一方的公共分数成比例的独立生成的偏好。我们计算预期的平均排名，在每一层的代理人有他们的合作伙伴在男性最佳的稳定匹配，并证明浓度的平均排名在渐近大市场的结果。此外，我们表明，尽管有显着的影响排名，公共分数并没有强烈影响代理匹配到另一方的给定层的概率。这推广了[Pittel 1989]的结果，这些结果对应于统一偏好。结果定量地证明了竞争的影响，由于在市场上的代理商的异质吸引力，我们给出了第一个明确的计算排名超越统一的市场。
英文摘要：
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.
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