论文标题
在匹配市场的合作伙伴的竞争
The Competition for Partners in Matching Markets
论文作者
论文摘要
我们研究了具有异质代理偏好的双面匹配市场中合作伙伴的竞争，重点是平衡结果如何取决于市场的连通性。我们对随机连接的市场进行建模，每个代理具有随机（无方向性）图的平均度$ D $，并且在图中的邻居比邻居的均匀随机偏好排名。我们正式地描述了大型市场中稳定的匹配随机的稳定匹配，并且在$ \ \ log^2 n $（$ n $是市场上一侧的代理商人数）中找到阈值$ d $），从而使“弱势竞争”方案分开，在市场上相同的情况下，在一个强大的竞争方面，它在很大程度上是一个重要的竞争机构，在这种情况下，很长一段竞争的情况，很长一段地）。 （缺点）。数值模拟确认并提高了我们的理论预测，并证明了对我们的假设的鲁棒性。我们通过两种方式利用我们的特征：首先，我们获得了有关如何设计市场连接以在获得的普通代理商福利和在市场上保持无与伦比的代理商数量之间进行最佳权衡的规定见解。对于大多数市场基础，我们发现最佳连通性应在于弱势竞争制度或政权之间的门槛。其次，我们的分析发现了一个新的概念原则，该原则是，在给定的匹配市场中，短方面的优势是否具有重要优势，此外，仅在给定市场的基本摘要统计信息下，它还可以用作诊断工具。使用有关在美国主要城市中集中式高中录取的数据进行的反事实分析表明，我们的设计见解和诊断原则的实践价值。
We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets, with each agent having an average degree $d$ in a random (undirected) graph, and a uniformly random preference ranking over their neighbors in the graph. We formally characterize stable matchings in large markets random with small imbalance and find a threshold in the connectivity $d$ at $\log^2 n$ (where $n$ is the number of agents on one side of the market) which separates a ``weak competition'' regime, where agents on both sides of the market do equally well, from a ``strong competition'' regime, where agents on the short (long) side of the market enjoy a significant advantage (disadvantage). Numerical simulations confirm and sharpen our theoretical predictions, and demonstrate robustness to our assumptions. We leverage our characterizations in two ways: First, we derive prescriptive insights into how to design the connectivity of the market to trade off optimally between the average agent welfare achieved and the number of agents who remain unmatched in the market. For most market primitives, we find that the optimal connectivity should lie in the weak competition regime or at the threshold between the regimes. Second, our analysis uncovers a new conceptual principle governing whether the short side enjoys a significant advantage in a given matching market, which can moreover be applied as a diagnostic tool given only basic summary statistics for the market. Counterfactual analyses using data on centralized high school admissions in a major USA city show the practical value of both our design insights and our diagnostic principle.
