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

TL;DR

This paper explores two-sided manipulation strategies in matching markets, developing polynomial algorithms for optimal manipulation, and demonstrating their increased frequency and quality over one-sided strategies.

Contribution

It introduces two new models for two-sided manipulation in matching markets and provides polynomial-time algorithms for finding optimal strategies in these models.

Findings

Two-sided manipulations are more common and effective than one-sided ones.

Polynomial algorithms successfully identify optimal manipulations.

Manipulation strategies can preserve stability under certain conditions.

Abstract

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.