The paper focuses on the basic one-to-one two-sided matching model, where there are two disjoint sets of agents of equal size, and each agent in a set has preferences on the agents in the other set, modeled by linear orders. The goal is to find a matching that associates each agent in one set with one and only one agent in the other set based on the agents' preferences.
The authors introduce the concept of symmetric matching mechanisms, which relates to fairness. A matching mechanism is symmetric if a change in the identities of the individuals results in the same change in the output. The authors consider different levels of symmetry, such as anonymity (equal treatment within each group) and gender fairness (equal treatment across the two groups).
The main results include:
The authors use notions and techniques from group theory to prove these results, which is a novel approach in matching theory.
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by Daniela Bubb... at arxiv.org 04-03-2024
https://arxiv.org/pdf/2404.01404.pdfDeeper Inquiries