Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings


  • Alireza Farhadi University of Maryland
  • MohammadTaghi Hajiaghayi University of Maryland
  • Mohamad Latifian University of Toronto
  • Masoud Seddighin Sharif University of Technology
  • Hadi Yami Microsoft



Fair Division


Envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) are two well-known extensions of envy-freeness for the case of indivisible items. It is shown that EF1 can always be guaranteed for agents with subadditive valuations. In sharp contrast, it is unknown whether or not an EFX allocation always exists, even for four agents and additive valuations. In addition, the best approximation guarantee for EFX is (φ − 1) ≃ 0.61 by Amanitidis et al.. In order to find a middle ground to bridge this gap, in this paper we suggest another fairness criterion, namely envy-freeness up to a random good or EFR, which is weaker than EFX, yet stronger than EF1. For this notion, we provide a polynomial-time 0.73-approximation allocation algorithm. For our algorithm we introduce Nash Social Welfare Matching which makes a connection between Nash Social Welfare and envy freeness.




How to Cite

Farhadi, A., Hajiaghayi, M., Latifian, M., Seddighin, M., & Yami, H. (2021). Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6), 5355-5362.



AAAI Technical Track on Game Theory and Economic Paradigms