Two-Sided Manipulation Games in Stable Matching Markets

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.

@article{hosseini2025_2506.00554,
  title={ Two-Sided Manipulation Games in Stable Matching Markets },
  author={ Hadi Hosseini and Grzegorz Lisowski and Shraddha Pathak },
  journal={arXiv preprint arXiv:2506.00554},
  year={ 2025 }
}