We adopt the notion of von Neumann-Morgenstern (vNM) farsightedly stable sets to determine which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of vNM farsightedly stable sets: a set of matchings is a vNM farsightedly...

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set. For the special cases where all players are myopic and where all players are farsighted, our concept predicts the set...