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On Fair Division for Indivisible Items

Authors Bhaskar Ray Chaudhury, Yun Kuen Cheung, Jugal Garg, Naveen Garg, Martin Hoefer, Kurt Mehlhorn

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Author Details

Bhaskar Ray Chaudhury
  • MPI for Informatics, Saarland Informatics Campus, Germany
Yun Kuen Cheung
  • Singapore University of Technology and Design, Singapore
Jugal Garg
  • Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, USA
Naveen Garg
  • Department of Computer Science, IIT Delhi, India
Martin Hoefer
  • Institut für Informatik, Goethe-Universität Frankfurt am Main, Germany
Kurt Mehlhorn
  • MPI for Informatics, Saarland Informatics Campus, Germany

Funding

  • Cheung, Yun Kuen: Most work done while the author was at MPI for Informatics, Saarland Informatics Campus. The author would like to acknowledge NRF 2018 Fellowship NRF-NRFF2018-07.
  • Garg, Jugal: Supported by NSF CRII Award 1755619.

Cite AsGet BibTex

Bhaskar Ray Chaudhury, Yun Kuen Cheung, Jugal Garg, Naveen Garg, Martin Hoefer, and Kurt Mehlhorn. On Fair Division for Indivisible Items. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2018.25

Abstract

We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of e^{1/{e}} ~~ 1.445. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of 2 + epsilon.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Fair Division
  • Indivisible Goods
  • Envy-Free

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