Equivalent Choice Functions and Stable Mechanisms

Abstract

We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism.Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds. JEL-classification: C78, D47

Cadet-Branch Matching in a Kelso-Crawford Economy

“…Substitutability is crucial to matching with contracts (Hatfield and Kojima 2008;Kominers 2012, 2017;Hatfield et al 2013;and Schlegel 2019). This paper shows that even choice functions that exhibit complementarities might be effectively substitutable from the perspective of matching mechanisms (DA-substitutable).…”