Rationalizable Behavior in Matching with Externalities

In many matching markets, agents care not only about their own partners but also about the matches formed by others. With externalities, stability depends on what agents believe would happen after a deviation. We introduce rationalizable conjectures: beliefs that survive iterated elimination, in the spirit of rationalizability in non-cooperative games. These beliefs define conjecture-rationalizable stability, a solution concept that always exists, extends Gale--Shapley stability, and coincides with it when externalities are absent. We also introduce rationalizable matchings, a non-equilibrium counterpart, and show that every conjecture-rationalizable stable matching is rationalizable. In matching with couples, our concept yields non-empty predictions even when standard stability is vacuous. Finally, we provide an epistemic foundation: rationalizability is behaviorally implied by pairwise rationality and common belief in pairwise rationality, while conjecture-rationalizable stability additionally requires belief correctness.