Strategyproof Pareto-Stable Mechanisms for Two-Sided Matching with Indifferences

TL;DR

This paper introduces new polynomial-time, strategyproof algorithms for Pareto-stable matchings in two-sided markets with indifferences, improving fairness and strategic resistance for one side of the market.

Contribution

The authors develop novel strategyproof Pareto-stable mechanisms for stable marriage and college admissions with weak preferences, addressing limitations of previous algorithms.

Findings

Algorithm for stable marriage is strategyproof for one side.

Algorithm for college admissions is strategyproof for students.

Both algorithms run in polynomial time.

Abstract

We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the problems that we address, previous authors have presented polynomial-time algorithms for computing a "Pareto-stable" matching. In the case of college admissions, these algorithms require the preferences of the colleges over groups of students to satisfy a technical condition related to responsiveness. We design new polynomial-time Pareto-stable algorithms for stable marriage and college admissions that correspond to strategyproof mechanisms. For stable marriage, it is known that no Pareto-stable mechanism is strategyproof for all of the agents; our algorithm provides a mechanism that is strategyproof for the agents on one side of the market. For college admissions, it is known that no Pareto-stable mechanism can be strategyproof for the colleges; our algorithm provides a mechanism that is strategyproof for the students.