[UTMD-075] Stable matching under inconsistent choice functions (by Keisuke Bando, Toshiyuki Hirai, Kenzo Imamura)

Keisuke Bando, Toshiyuki Hirai, Kenzo Imamura

We study stable matching in the many to one matching model. Substitutability, together with consistency, is known to guarantee the existence of a stable matching. We first observe that in certain applications a stable matching still exists even in the absence of consistency. We then introduce a weaker condition, monotonicity, and show that the combination of substitutability and monotonicity ensures the existence of a stable matching. Consistency is the rationalization axiom introduced in the choice theory literature. Our result suggests that rationalization is not necessarily required in stable matching theory. Furthermore, we analyze a stable and strategy-proof mechanism, focusing on the cumulative offer process, which is widely used in both theory and practice. We derive a necessary condition for the cumulative offer process to be stable and strategy-proof under substitutable and weakly monotonic choice functions for any proposal order, provided that there are sufficiently many doctors. This condition is stringent, highlighting that the addition of strategy-proofness imposes significant restrictions. We apply our conditions to real-life applications such as daycare allocation and college admissions.