Testing Substitutability of Weak Preferences

TL;DR

This paper extends an algorithm to test substitutability of weak preferences in many-to-many matching models, demonstrating improved speed over previous methods for strict preferences, thereby aiding the analysis of stable matchings.

Contribution

It introduces an extension of Hatfield et al.'s algorithm to handle weak preferences and shows it is faster than the original for strict preferences.

Findings

The extended algorithm correctly tests substitutability of weak preferences.

The new algorithm outperforms previous methods on strict preferences.

Speed improvement is linear in the domain of strict preferences.

Abstract

In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test substitutability of weak preferences. Interestingly, the algorithm is faster than the algorithm of Hatfield et al. by a linear factor on the domain of strict preferences.