Do stable outcomes survive in marriage problems with myopic and farsighted players?

Abstract

We consider marriage problems where myopic and farsighted players interact and analyze these problems by means of the myopic-farsighted stable set. We require that coalition members are only willing to deviate if they all strictly benefit from doing so. Our first main result establishes the equivalence of myopic-farsighted stable sets based on arbitrary coalitional deviations and those based on pairwise deviations.

We are interested in the question whether the core is still the relevant solution concept when myopic and farsighted agents interact and whether more farsighted agents are able to secure more preferred core elements. For marriage problems where all players are myopic as well as those where all players are farsighted, myopic-farsighted stable sets lead to the same prediction as the core. The same result holds for $\alpha$-reducible marriage problems, without any assumptions on the set of farsighted agents. These results change when one side of the market is more farsighted than the other. For general marriage problems where all women are farsighted, only one core element can be part of a myopic-farsighted stable set, the woman-optimal stable matching. If the woman-optimal stable matching is dominated from the woman point of view by an individually rational matching, then no core element can be part of a myopic-farsighted stable set.