General Manipulability Theorem for a Matching Model

TL;DR

This paper proves a general manipulability theorem for a many-to-many matching model under specific preference conditions, extending previous results and highlighting limitations when certain assumptions are relaxed.

Contribution

It generalizes the Manipulability Theorem from many-to-one to many-to-many matching models under substitutability and the law of aggregate demand.

Findings

Theorem holds under substitutability and aggregate demand laws.

Theorem fails if only substitutability is assumed.

Extends previous matching theory results.

Abstract

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we proof the General Manipulability Theorem. We result generalizes the presented in Sotomayor (1996 and 2012) for the many-to-one model. In addition, we show General Manipulability Theorem fail when agents' preferences satisfy only substitutability.