Obvious Manipulations in Matching without and with Contracts

R. Pablo Arribillaga; E. Pepa Risma

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arXiv · 2306.17773

Obvious Manipulations in Matching without and with Contracts

R. Pablo Arribillaga·E. Pepa Risma

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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.

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R. Pablo Arribillaga, E. Pepa Risma. 2024-10-16. Obvious Manipulations in Matching without and with Contracts. https://arxiv.org/abs/2306.17773

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