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Competitive Auctions and Envy-Freeness for Group of Agents

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Computing and Combinatorics (COCOON 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

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Abstract

In mechanism design, fairness is one of the central criteria for analyzing mechanisms. Recently, a new fairness concept called envy-freeness of a group toward a group (GtG-EFness) has received attention, which requires that no group of agents envies any other group. In this paper, we consider GtG-EFness in more general combinatorial auctions, including several subclasses of the multi-unit auction domain (unit-demand, diminishing marginal values, and all-or-nothing), and reveal the tight bound of the competitive ratios. In particular, we prove that the tight bound of the competitive ratio is 1/k (where k is the number of items) for the general combinatorial auction domain. We also clarify the relationship with Walrasian equilibria and conclude that no group envies any other group in any Walrasian equilibrium.

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Notes

  1. 1.

    We abbreviate the GCA domain as GCA interchangeably, and the others as well.

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Acknowledgments

This work is partially supported by JSPS KAKENHI Grants JP17H00761 and JP17H04695. The authors thank Takayuki Mouri for his helpful comments and discussions. All errors are our own.

Author information

Authors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Taiki Todo & Makoto Yokoo

  2. The University of Electro-Communications, Chofu, Japan

    Atsushi Iwasaki

  3. RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan

    Taiki Todo, Atsushi Iwasaki & Makoto Yokoo

Authors
  1. Taiki Todo
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  2. Atsushi Iwasaki
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  3. Makoto Yokoo
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Corresponding author

Correspondence to Taiki Todo .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Todo, T., Iwasaki, A., Yokoo, M. (2019). Competitive Auctions and Envy-Freeness for Group of Agents. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_45

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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