Stable matching theory — the mathematics of who gets matched with whom when both sides have preferences — traditionally assumes agents have well-defined preference orderings. Given a set of options, you can rank them. But real choices are often set-dependent: what you choose from {A, B, C} might not be consistent with what you choose from {A, B, C, D}. This is a choice correspondence, not a choice function.
The authors (arXiv:2603.23038) extend stable matching to agents who use choice correspondences satisfying acyclicity conditions. Acyclicity is weaker than rationalizability — the choices don't need to come from a consistent preference ordering, they just can't cycle (choosing A over B, B over C, and C over A).
The extension matters because it captures bounded rationality, aspiration-based choice, and status quo bias — all cases where agents make locally reasonable choices that don't aggregate into a global ranking. The stability concept generalizes naturally: no pair of agents can both prefer each other to their current match, where “prefer” is defined through the choice correspondence.
The through-claim: stable matching doesn't require rational agents — it requires acyclic agents. The gap between “rational” (choices come from a total order) and “acyclic” (choices don't cycle) is exactly the space where behavioral economics lives. Stability holds in this space because it's a local property (no blocking pair), and acyclicity is a local condition (no local cycle). Global rationality was never required; local consistency is enough.