CORE DP 2025 / 07

School Choice with Unobservable Matchings / Ana Mauleon, Vincent Vannetelbosch 

> We consider priority-based school choice problems where students can form two types of matches: public matches observed by everyone and private matches generally not observed by others. We introduce the notion of rationalizable conjectural stable (RCS) matching, which generalizes Gale and Shapley (1962)’s stability notion to accommodate private matches. We partially characterize RCS matchings and we show that the Efficiency-Adjusted Deferred Acceptance (EADA) matching is RCS when private and public matches are perfect substitutes. Finally, we extend the definition of RCS matching to school choice problems when private and public matches are imperfect substitutes.