Bribery and Control in Stable Marriage

TL;DR

This paper explores the computational complexity of external manipulations in the Stable Marriage problem, analyzing various manipulation strategies and goals, and identifying both polynomial-time solvable and NP-hard cases.

Contribution

It provides a comprehensive complexity analysis of manipulation problems in Stable Marriage, including parameterized complexity results for various manipulation scenarios.

Findings

Several polynomial-time solvable manipulation problems.

Many manipulation problems are NP-hard.

Parameterized complexity results show hardness with respect to manipulation budget.

Abstract

We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable solution, and this may be achieved by the manipulative action of reordering some agents' preference lists. We present a comprehensive study of the computational complexity of all problems arising in this way. We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard cases, focusing on the natural parameter budget (that is, the number of manipulative actions one is allowed to perform), we also conduct a parameterized complexity analysis and encounter mostly parameterized hardness results.