Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination


  • Georgios Amanatidis Sapienza University of Rome
  • Evangelos Markakis Athens University of Economics and Business
  • Apostolos Ntokos Athens University of Economics and Business



Several relaxations of envy-freeness, tailored to fair division in settings with indivisible goods, have been introduced within the last decade. Due to the lack of general existence results for most of these concepts, great attention has been paid to establishing approximation guarantees. In this work, we propose a simple algorithm that is universally fair in the sense that it returns allocations that have good approximation guarantees with respect to four such fairness notions at once. In particular, this is the first algorithm achieving a (φ−1)-approximation of envy-freeness up to any good (EFX) and a 2/φ+2 -approximation of groupwise maximin share fairness (GMMS), where φ is the golden ratio. The best known approximation factor, in polynomial time, for either one of these fairness notions prior to this work was 1/2. Moreover, the returned allocation achieves envy-freeness up to one good (EF1) and a 2/3-approximation of pairwise maximin share fairness (PMMS). While EFX is our primary focus, we also exhibit how to fine-tune our algorithm and improve further the guarantees for GMMS or PMMS.

Finally, we show that GMMS—and thus PMMS and EFX—allocations always exist when the number of goods does not exceed the number of agents by more than two.




How to Cite

Amanatidis, G., Markakis, E., & Ntokos, A. (2020). Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination. Proceedings of the AAAI Conference on Artificial Intelligence, 34(02), 1790-1797.



AAAI Technical Track: Game Theory and Economic Paradigms