社交网络与就业市场的稳定匹配
Social Networks and Stable Matchings in the Job Market
摘要：
对大多数人来说，社会关系在找新工作中起着不可或缺的作用。正如格兰米特的开创性研究所观察到的那样，通过社会关系获得的工作比例通常比通过职位或机构获得的工作比例大。与此同时，就业市场是双边匹配市场的一个自然例子。在这样的市场中，一个重要的解决方案概念是稳定匹配，并使用著名的Gale-Shapley算法来计算它们。到目前为止，文献已经分别发展，要么集中在信息流动通过社会网络的影响，或通过使用双边匹配技术发展就业市场的数学理论。在本文中，我们提供了一个就业市场模型，将就业市场的两个方面结合在一起。为了模拟社会科学家的观察结果，我们假设工人只通过社会接触了解公司的职位。鉴于这种信息结构，我们研究了我们称之为局部稳定匹配的静态特性（即，稳定的匹配受到社会网络给出的信息约束）和动态属性，通过重新解释盖尔-夏普利的算法作为近视的最佳反应动力学。我们证明了，在一般情况下，局部稳定匹配的集合严格包含稳定匹配的集合，并且确定它们是否相同实际上是NP-完全的。我们还表明，稳定匹配的晶格结构一般是不存在的。最后，我们专注于近视的最佳反应动力学的启发Gale-Shapley算法。我们研究了由于信息约束的效率损失，提供了下限和上限。
英文摘要：
For most people, social contacts play an integral part in finding a new job. As observed by Granovetter's seminal study, the proportion of jobs obtained through social contacts is usually large compared to those obtained through postings or agencies. At the same time, job markets are a natural example of two-sided matching markets. An important solution concept in such markets is that of stable matchings, and the use of the celebrated Gale-Shapley algorithm to compute them. So far, the literature has evolved separately, either focusing on the implications of information flowing through a social network, or on developing a mathematical theory of job markets through the use of two-sided matching techniques. In this paper we provide a model of the job market that brings both aspects of job markets together. To model the social scientists' observations, we assume that workers learn only about positions in firms through social contacts. Given that information structure, we study both static properties of what we call locally stable matchings (i.e., stable matchings subject to informational constraints given by a social network) and dynamic properties through a reinterpretation of Gale-Shapley's algorithm as myopic best response dynamics. We prove that, in general, the set of locally stable matching strictly contains that of stable matchings and it is in fact NP-complete to determine if they are identical. We also show that the lattice structure of stable matchings is in general absent. Finally, we focus on myopic best response dynamics inspired by the Gale-Shapley algorithm. We study the efficiency loss due to the informational constraints, providing both lower and upper bounds.
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