关于合并Sharply-Scarf房地产市场(cs.GT)---用户7199428

我们研究合并Sharply-Scarf房地产市场的好的影响。我们为受合并影响的代理商数量与他们遭受的损失程度加上了严格的限界。我们发现在最糟糕的情形下，市场合并会损害大部分的代理商的利益，并且代理商的房子的平均排名会跌落达到排行榜长度的50%。我们同样统计了平均情况。我们准确计算出了市场随机合并时能带来的预期收益，并且统一进行了优先列表的随机选取。可以看出，平均来讲，市场合并对于所有的代理商来说是有利的，尤其是那些处在较小市场中的代理商。通过使用首位交易算法（TTC）的预计循环次数，我们给受合并损害的预计代理商数量加上了限界。特别的是，如果每一个市场有着同样的大小，预计受合并损害的代理商比例将少于50%，并且少于26个（这儿数值并不受合并市场数量的影响）。我们由此得出，在挑选偏好域的前提下，就能确保受市场合并损害的代理商只是少数。

原文题目：On the integration of Shapley-Scarf housing markets

原文：We study the welfare consequences of merging disjoint Shapley-Scarf housing markets. We obtain tight bounds on the number of agents harmed by integration and on the size of their losses. We show that, in the worst-case scenario, market integration may harm the vast majority of agents, and that the average rank of an agent's house can decrease (asymptotically) by 50% of the length of their preference list. We also obtain average-case results. We exactly compute the expected gains from integration in random markets, where each of the preference profiles is chosen uniformly at random. We show that, on average, market integration benefits all agents, particularly those in smaller markets. Using the expected number of cycles in the top trading cycles algorithm, we bound the expected number of agents harmed by integration. In particular, the expected fraction of agents harmed by integration is less than 50% if each market has the same size and this is below 26 (independent of the number of markets that merge). We conclude by providing a preference domain that ensures that those harmed by market integration are a minority.

原文作者：Rajnish Kunar, Kriti Manocha, Josue Ortega

原文地址：https://arxiv.org/abs/2004.09075