Obvious Manipulations in Matching without and with 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 \textit{obvious manipulations} and identifies stable-dominating mechanisms that prevent them. Without contracts, we show that more efficient mechanisms are less likely to be obviously manipulable and 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.
Keywords
Cite
@article{arxiv.2306.17773,
title = {Obvious Manipulations in Matching without and with Contracts},
author = {R. Pablo Arribillaga and E. Pepa Risma},
journal= {arXiv preprint arXiv:2306.17773},
year = {2024}
}