Two-Sided Matching Meets Fair Division
This work addresses fairness in multi-agent matching problems, such as resource allocation or job markets, but is incremental as it adapts existing fair division ideas to a new matching model.
The paper tackles the problem of combining two-sided matching with fairness concepts from fair division, introducing new fairness notions like double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). It shows that DEF1 can be achieved in a special case using a round-robin algorithm, while DMMS is impossible even under identical preferences.
We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.