Obvious manipulations in matching with and without contracts

Abstract

This paper explores many-to-one matching models, both with and without contracts, where doctors' preferences are private and hospitals' preferences are public and substitutable. It is known that any stable-dominating mechanism –which is either stable or individually rational and Pareto-dominates (from the doctors' perspective) a stable mechanism–, is susceptible to manipulation by doctors. Our study focuses on obvious manipulations and identifies stable-dominating mechanisms that prevent them. Without contracts, we show that any stable-dominating mechanism is not obviously manipulable. However, with contracts, none of these results hold. While we demonstrate that the Doctor-Proposing Deferred Acceptance (DA) Mechanism remains not obviously manipulable, we show that the Hospital-Proposing DA Mechanism and any efficient mechanism that Pareto-dominates the Doctor-Proposing DA Mechanism become (very) obviously manipulable, in the model with contracts.