Do Stable Outcomes Survive in Marriage Problems with Myopic and Farsighted Players?

We consider marriage problems where myopic and farsighted players interact. To study such problems, we use the pairwise myopic-farsighted stable set. Blocking occurs by coalitions of size one or two. We require that all blocking players should strictly improve. We pay particular attention to the question whether core elements survive in this environment. This is the case when all players are myopic as well as when all players are farsighted. It also holds for matching problems satisfying the top-coalition property. For general matching problems where all women are farsighted, there is only one core element that can belong to the pairwise myopic-farsighted stable set, the woman-optimal stable matching, so all other stable outcomes are excluded for sure. If the woman-optimal stable matching is dominated from the woman point of view by an individually rational matching, then the pairwise myopic farsighted stable set cannot contain a core element. We show that blocking by coalitions of arbitrary size leads to identical results.