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Fair allocation of indivisible goods: Improvement

Ghodsi, M ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1287/MOOR.2020.1096
  3. Publisher: INFORMS Inst.for Operations Res.and the Management Sciences , 2021
  4. Abstract:
  5. We study the problem of fair allocation for indivisible goods. We use the maximin share paradigm introduced by Budish [Budish E (2011) The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. J. Political Econom. 119(6):1061-1103.] as a measure of fairness. Kurokawa et al. [Kurokawa D, Procaccia AD, Wang J (2018) Fair enough: Guaranteeing approximate maximin shares. J. ACM 65(2):8.] were the first to investigate this fundamental problem in the additive setting. They showed that in delicately constructed examples, not everyone can obtain a utility of at least her maximin value. They mitigated this impossibility result with a beautiful observation: no matter how the utility functions are made, we always can allocate the items to the agents to guarantee each agent's utility is at least 2/3 of her maximin value. They left open whether this bound can be improved. Our main contribution answers this question in the affirmative. We improve their approximation result to a 3/4 factor guarantee. © 2021 INFORMS
  6. Keywords:
  7. Computer applications ; Research ; Approximation results ; Combinatorial assignment ; Competitive equilibrium ; Fair allocation ; Impossibility results ; Indivisible good ; Maximin ; Utility functions ; Combinatorial optimization
  8. Source: Mathematics of Operations Research ; Volume 46, Issue 3 , 2021 , Pages 1038-1053 ; 0364765X (ISSN)
  9. URL: https://pubsonline.informs.org/doi/abs/10.1287/moor.2020.1096