Accomplice Manipulation of the Deferred Acceptance Algorithm

TL;DR

This paper introduces a new model of strategic manipulation in the deferred acceptance algorithm involving an accomplice, providing algorithms and analysis of its effectiveness and stability implications.

Contribution

It presents the concept of accomplice manipulation, characterizes optimal strategies, and offers polynomial algorithms to identify such manipulations.

Findings

Optimal accomplice manipulation involves promoting exactly one woman.

Polynomial-time algorithm for computing optimal accomplice manipulation.

Accomplice manipulation is more frequent and yields better matches than self manipulation.

Abstract

The deferred acceptance algorithm is an elegant solution to the stable matching problem that guarantees optimality and truthfulness for one side of the market. Despite these desirable guarantees, it is susceptible to strategic misreporting of preferences by the agents on the other side. We study a novel model of strategic behavior under the deferred acceptance algorithm: manipulation through an accomplice. Here, an agent on the proposed-to side (say, a woman) partners with an agent on the proposing side -- an accomplice -- to manipulate on her behalf (possibly at the expense of worsening his match). We show that the optimal manipulation strategy for an accomplice comprises of promoting exactly one woman in his true list (i.e., an inconspicuous manipulation). This structural result immediately gives a polynomial-time algorithm for computing an optimal accomplice manipulation. We also study the conditions under which the manipulated matching is stable with respect to the true preferences. Our experimental results show that accomplice manipulation outperforms self manipulation both in terms of the frequency of occurrence as well as the quality of matched partners.