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Competitive VCG Redistribution Mechanism for Public Project Problem

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Book cover PRIMA 2016: Principles and Practice of Multi-Agent Systems (PRIMA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9862))

Abstract

The VCG mechanism has many nice properties, and can be applied to a wide range of social decision problems. One problem of the VCG mechanism is that even though it is efficient, its social welfare (agents’ total utility considering payments) can be low due to high VCG payments. VCG redistribution mechanisms aim to resolve this by redistributing the VCG payments back to the agents. Competitive VCG redistribution mechanisms have been found for various resource allocation settings. However, there has been almost no success outside of the scope of allocation problems. This paper focuses on another fundamental model - the public project problem. In Naroditskiy et al. 2012, it was conjectured that competitive VCG redistribution mechanisms exist for the public project problem, and one competitive mechanism was proposed for the case of three agents (unfortunately, both the mechanism and the techniques behind it do not generalize to cases with more agents). In this paper, we propose a competitive mechanism for general numbers of agents, relying on new techniques.

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Notes

  1. 1.

    The VCG mechanism always picks the outcome that maximizes the agents’ total valuation.

  2. 2.

    By social welfare, we mean the agents’ total utility: total valuation minus total payment.

  3. 3.

    Even for n between 4 and 6, there is no guarantee of worst-case performance, because the worst-case is simulated via sampling, which may not be extensive enough.

  4. 4.

    We do need the minor assumption that the number of agents is large compared to the number of items.

  5. 5.

    If \(\sum _{j\ne i}\theta _j\ge \frac{n-1}{n}\), then pick \(\theta _i'=1\). Otherwise, pick \(\theta _i'=0\).

  6. 6.

    This is called revenue monotonicity.

  7. 7.

    The fourth term of E stays the same.

  8. 8.

    Term one and three cancel out.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Adelaide, Adelaide, Australia

    Mingyu Guo

Authors
  1. Mingyu Guo
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Correspondence to Mingyu Guo .

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Torino , Torino, Italy

    Matteo Baldoni

  2. Computing and Communications, Lancaster University, Lancaster, United Kingdom

    Amit K. Chopra

  3. Department of Computer Science, New Mexico State University, Las Cruces, New Mexico, USA

    Tran Cao Son

  4. Graduate School of Maritime Sciences, Kobe University, Kobe, Japan

    Katsutoshi Hirayama

  5. Dept. di Informatica: Sci. e Ingegneria, Universitá di Bologna, Bologna, Italy

    Paolo Torroni

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Guo, M. (2016). Competitive VCG Redistribution Mechanism for Public Project Problem. In: Baldoni, M., Chopra, A., Son, T., Hirayama, K., Torroni, P. (eds) PRIMA 2016: Principles and Practice of Multi-Agent Systems. PRIMA 2016. Lecture Notes in Computer Science(), vol 9862. Springer, Cham. https://doi.org/10.1007/978-3-319-44832-9_17

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  • DOI: https://doi.org/10.1007/978-3-319-44832-9_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44831-2

  • Online ISBN: 978-3-319-44832-9

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