Two-Sided Manipulation Games in Stable Matching Markets

TL;DR

This paper explores non-cooperative manipulation strategies in stable matching markets, introducing algorithms to find equilibria that can improve outcomes for specific agents while maintaining stability.

Contribution

It introduces the accomplice manipulation game, provides a polynomial-time algorithm for finding Nash equilibria, and applies these techniques to various manipulation scenarios in matching markets.

Findings

Algorithm always finds a stable matching at equilibrium

Not all Nash equilibria correspond to stable matchings

Empirical analysis of agent welfare in manipulated matchings

Abstract

The Deferred Acceptance (DA) algorithm is an elegant procedure for finding a stable matching in two-sided matching markets. It ensures that no pair of agents prefers each other to their matched partners. In this work, we initiate the study of two-sided manipulations in matching markets as non-cooperative games. We introduce the accomplice manipulation game, where a man misreports to help a specific woman obtain a better partner, whenever possible. We provide a polynomial time algorithm for finding a pure strategy Nash equilibrium (NE) and show that our algorithm always yields a stable matching - although not every Nash equilibrium corresponds to a stable matching. Additionally, we show how our analytical techniques for the accomplice manipulation game can be applied to other manipulation games in matching markets, such as one-for-many and the standard self-manipulation games. We complement our theoretical findings with empirical evaluations of different properties of the resulting NE, such as the welfare of the agents.