Professional networks -- the social networks among people in a given line of work -- can serve as a conduit for job prospects and other opportunities. Here we propose a model for the formation of such networks and the transfer of opportunities within them. In our theoretical model, individuals strategically connect with others to maximize the probability that they receive opportunities from them. We explore how professional networks balance connectivity, where connections facilitate opportunity transfers to those who did not get them from outside sources, and congestion, where some individuals receive too many opportunities from their connections and waste some of them. We show that strategic individuals are over-connected at equilibrium relative to a social optimum, leading to a price of anarchy for which we derive nearly tight asymptotic bounds. We also show that, at equilibrium, individuals form connections to those who provide similar benefit to them as they provide to others. Thus, our model provides a microfoundation in professional networking contexts for the fundamental sociological principle of homophily, that "similarity breeds connection," which in our setting is realized as a form of status homophily based on alignment in individual benefit. We further explore how, even if individuals are a priori equally likely to receive opportunities from outside sources, equilibria can be unequal, and we provide nearly tight bounds on how unequal they can be. Finally, we explore the ability for online platforms to intervene to improve social welfare and show that natural heuristics may result in adverse effects at equilibrium. Our simple model allows for a surprisingly rich analysis of coordination problems in professional networks and suggests many directions for further exploration.

翻译：专业网络——同一行业人员间的社交网络——可作为工作机会及其他机遇的传递渠道。本文提出一个关于此类网络形成及机会在其中传递的模型。在理论模型中，个体为最大化从他人处获得机会的概率而策略性地建立联系。我们探讨了专业网络如何平衡连通性与拥塞效应：一方面，联系有助于将外部来源未获得的机会转移给其他人；另一方面，某些个体从联系中接收过多机会导致部分机会被浪费。研究表明，相较于社会最优状态，策略性个体在均衡状态下存在过度连接现象，由此产生我们推导出近似紧渐近界的"无序代价"。我们还发现，在均衡状态下，个体倾向于与那些能为自己提供与自身给予他人相似收益的人建立联系。因此，该模型为社会学基本同质性原理（"相似性孕育连接"）提供了专业网络情境下的微观基础——在我们的设定中以个体收益匹配为基础的地位同质性形式呈现。进一步研究表明，即使个体先验地从外部来源获得机会的概率相等，均衡状态仍可能呈现不平等性，我们给出了这种不平等程度的近似紧界。最后，我们探讨了在线平台通过干预改善社会福利的能力，并发现自然启发式策略可能在均衡状态下产生负面效应。这个简洁模型对专业网络中的协调问题提出了令人惊讶的丰富分析，并为后续研究提供了诸多方向。