Rationalizable Behavior in Matching with Externalities

Abstract: 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.