Social Welfare in One-Sided Matching Mechanisms

TL;DR

This paper analyzes the efficiency loss in one-sided matching mechanisms, establishing bounds on their Price of Anarchy and Price of Stability, and demonstrating that well-known mechanisms are optimal within these bounds.

Contribution

It provides the first general lower bound on the Price of Anarchy for all mechanisms in one-sided matching, and shows that Probabilistic Serial and Random Priority are optimal.

Findings

Lower bound of Ω(√n) on Price of Anarchy for all mechanisms.

Probabilistic Serial and Random Priority achieve matching upper bounds.

Stronger bounds on Price of Anarchy for deterministic mechanisms.

Abstract

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms.