Abstract In matching problems with externalities, prudence measures the importance an agent gives to others’ potential reactions when she considers deviating and social connectedness measures others’ capacity to react to the agent’s deviation. Assuming that externalities and preferences are random, the roles of prudence and social connectedness are studied. It is shown that asymptotic stability—a property that never holds in the absence of externalities—is achieved when the product of social connectedness and prudence grows at least exponentially with the population. Since social connectedness increases quickly in both the marriage and roommates markets, stability obtains even when prudence vanishes (sufficiently slowly).

中文翻译：

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与外部性匹配：审慎和社会联系在稳定性中的作用

摘要 在匹配问题与外部性时，谨慎衡量代理人在考虑偏离时对其他人潜在反应的重要性，而社会联系则衡量他人对代理人的偏离作出反应的能力。假设外部性和偏好是随机的，则研究谨慎和社会联系的作用。结果表明，当社会联系和审慎的乘积至少随人口呈指数增长时，渐近稳定性——一种在没有外部性的情况下永远不会成立的特性——就会实现。由于婚姻和室友市场的社会联系迅速增加，即使谨慎消失（足够缓慢）也会获得稳定。