Two-Sided Manipulation Games in Stable Matching Markets

2025-05-31

AI Summary

This paper investigates *collusive manipulation* in stable matching markets: a male agent strategically misreports his preferences to improve the match quality of a specific female. We formalize, for the first time, a two-sided manipulation game and propose a polynomial-time algorithm to compute pure-strategy Nash equilibria, proving that all such equilibria yield stable matchings. Crucially, we establish that Nash equilibrium and stability are not equivalent: while every equilibrium outcome is stable, not every stable matching is an equilibrium outcome. We extend the framework to many-to-one collusion and self-manipulation variants. Through algorithmic design, complexity analysis, and large-scale simulations, we characterize welfare distribution among participants at equilibrium and validate algorithmic efficacy. Our core contribution is the first computationally tractable game-theoretic model of collusive manipulation in stable matching, bridging classical stability theory with strategic behavior analysis.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Study two-sided manipulations in matching markets as games
• Develop algorithm for Nash equilibrium in accomplice manipulation
• Apply techniques to other manipulation games in matching

Innovation

• Introduces accomplice manipulation game concept
• Provides polynomial time NE finding algorithm
• Applies techniques to various manipulation games