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.
翻译:我们研究双面匹配市场伙伴的竞争情况,这些市场具有不同的代理商的喜好,重点是平衡结果如何取决于市场的连通性。我们随机地模拟部分连接市场,每个代理商在随机(非方向)图中平均拥有美元美元,在图表中平均随机偏差排序。我们正式将大型市场中稳定匹配与小规模失衡相对称为稳定,并在连接值中找到一个门槛值,即美元为美元(美元是市场一面的基本代理商数目),这把“微弱竞争”制度区分开来,市场两边的代理商在“强竞争”制度上都做得同样好,在“强竞争”制度下,市场短(长)边的代理商享有显著优势(劣势 ), 数字模拟证实并强化了我们的理论预测,并显示了我们的假设力。 我们以两种方式利用我们的特征分析:首先,我们对如何设计市场在平均代理商福利方面实现的连通度如何最佳贸易关系,在“强势”原则下,在“激烈的市场设计者分析中应该更准确地反映我们最弱的市场结构,在市场中,在“最差的”的市场中应该发现,在“最弱的“最差的”的“最差的市场”中,在“最差的”的“最差值”的“最差的”中,在市场”的“最差的“最差值”的“最差值”的“最差值”中,在市场”的“最差值”的“最差值”的“我们“最差值是“最差值”的“最差值”的市场”的“最差值”中,在市场”的“最差值”的“最差值”的“最差值”的“最差值”的“最差值”中,在市场”中,在市场”的“最差值”中,在市场”的“最差值是“最差值是“最差值是“我们“最差值”中,在市场”的“最差值”的“最差值是“比。