Jiehua Chen

Paper accepted at EC 2019: Matchings under Preferences: Strength of Stability and Trade-Offs

Posted on by Jiehua Chen


We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962).

Informally speaking, robustness requires that a matching must be stable in the classic sense, even if the agents slightly change their preferences. Near stability, on the other hand, imposes that a matching must become stable (again, in the classic sense) provided the agents are willing to adjust their preferences a bit.

Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of trade-offs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined trade-offs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching, and we prove that finding a socially optimal and nearly stable matching is computationally hard.


The paper can be found on arXiv and on ACM DL. Slides presented at the EC’19 conference can be downloaded here. If you want to use them publicly, please ask for permission jiehua.chen@tuwien.ac.at