New algorithms for matching problems

TL;DR

This paper introduces new algorithms for matching problems, analyzing their fairness, social welfare, and axiomatic properties, and demonstrating that some outperform classic algorithms in welfare under truthful preferences.

Contribution

The paper presents novel matching algorithms with systematic derivation from existing ones, evaluating their welfare and axiomatic tradeoffs, and highlighting their potential advantages.

Findings

Some new algorithms outperform classic ones in welfare under truthful preferences.

New algorithms show promising fairness and efficiency tradeoffs.

Systematic derivation links 2-sided and 1-sided matching algorithms.

Abstract

The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the Gale-Shapley algorithm; for one-sided matching, (random) Serial Dictatorship and Probabilistic Serial rule; for school choice, Gale-Shapley and the Boston mechanisms. The main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of efficiency and strategyproofness. However if we shift the focus to fairness, social welfare, tradeoffs between incompatible axioms, and average-case analysis, it is far from clear that these algorithms are optimal. We investigate new algorithms several of which have not appeared (to our knowledge) in the literature before. We give a unified presentation in which algorithms for 2-sided matching yield 1-sided matching algorithms in a systematic way. In addition to axiomatic properties, we investigate agent welfare using both theoretical and computational approaches. We find that some of the new algorithms are worthy of consideration for certain applications. In particular, when considering welfare under truthful preferences, some of the new algorithms outperform the classic ones.