We consider marriage markets with externalities. We focus on weak externalities, that is, markets in which each agent is primarily concerned about her partner. We formalize and prove the claim that weak externalities are not so significant in the marriage market: in this case, the ω-core and the α-core coincide and are both nonempty. In addition, we show that, if we allow agents to block matchings without changing their mate, the results do not longer hold.

中文翻译：

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关于弱外部性婚姻市场的注解

我们考虑具有外部性的婚姻市场。我们关注弱外部性，即每个代理商主要关心其合作伙伴的市场。我们形式化并证明了弱外部性在婚姻市场中并不那么重要的主张：在这种情况下，ω-核心和α-核心重合并且都是非空的。此外，我们还表明，如果我们允许智能体在不改变其配偶的情况下阻止匹配，结果将不再成立。