Two for One & One for All: Two-Sided Manipulation in Matching Markets

Two for One & One for All: Two-Sided Manipulation in Matching Markets

Hadi Hosseini, Fatima Umar, Rohit Vaish

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence
Main Track. Pages 321-327. https://doi.org/10.24963/ijcai.2022/46

Strategic behavior in two-sided matching markets has been traditionally studied in a "one-sided" manipulation setting where the agent who misreports is also the intended beneficiary. Our work investigates "two-sided" manipulation of the deferred acceptance algorithm where the misreporting agent and the manipulator (or beneficiary) are on different sides. Specifically, we generalize the recently proposed accomplice manipulation model (where a man misreports on behalf of a woman) along two complementary dimensions: (a) the two for one model, with a pair of misreporting agents (man and woman) and a single beneficiary (the misreporting woman), and (b) the one for all model, with one misreporting agent (man) and a coalition of beneficiaries (all women). Our main contribution is to develop polynomial-time algorithms for finding an optimal manipulation in both settings. We obtain these results despite the fact that an optimal one for all strategy fails to be inconspicuous, while it is unclear whether an optimal two for one strategy satisfies the inconspicuousness property. We also study the conditions under which stability of the resulting matching is preserved. Experimentally, we show that two-sided manipulations are more frequently available and offer better quality matches than their one-sided counterparts.
Keywords:
Agent-based and Multi-agent Systems: Computational Social Choice
Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems