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The Pareto Frontier of Inefficiency in Mechanism Design

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Web and Internet Economics (WINE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11920))

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Abstract

We study the trade-off between the Price of Anarchy (PoA) and the Price of Stability (PoS) in mechanism design, in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to the above metrics, and observe that two fundamental mechanisms, namely the First-Price (FP) and the Second-Price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms \(\mathcal {SP}_\alpha \) that lie exactly on this frontier. In particular, these mechanisms range smoothly, with respect to parameter \(\alpha \ge 1\) across the frontier, between the First-Price (\(\mathcal {SP}_1\)) and Second-Price (\(\mathcal {SP}_\infty \)) mechanisms.

En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether non-truthful mechanisms can provide better makespan guarantees in the equilibrium, compared to truthful ones. We answer this question in the negative, by proving that the Price of Anarchy of all scheduling mechanisms is at least n, where n is the number of machines.

Supported by ERC Advanced Grant 321171 (ALGAME), the Swiss National Science Foundation under contract No. 200021_165522 and the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). A full version of this paper is available at [8].

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Notes

  1. 1.

    In the related literature, this mechanism is often referred to as the Vickrey-Clarke-Groves (VCG) mechanism.

  2. 2.

    We will be interested in pure Nash equilibria in this paper; we provide a discussion on different solution concepts in the full version.

  3. 3.

    For a more detailed discussion of anonymity and tie-breaking, see Remark 1 of the full version.

  4. 4.

    This is without loss of generality for our results; the tie-breaking could be any fixed total order on the machines that does not depend on the reports.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Aris Filos-Ratsikas

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Aris Filos-Ratsikas

  3. TU Munich, Munich, Germany

    Yiannis Giannakopoulos

  4. Sapienza University of Rome, Rome, Italy

    Philip Lazos

Authors
  1. Aris Filos-Ratsikas
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  2. Yiannis Giannakopoulos
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  3. Philip Lazos
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Corresponding author

Correspondence to Aris Filos-Ratsikas .

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Editors and Affiliations

  1. University of Patras, Rio, Greece

    Ioannis Caragiannis

  2. Google Research New York, New York, NY, USA

    Vahab Mirrokni

  3. The University of Texas System, Austin, TX, USA

    Evdokia Nikolova

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Filos-Ratsikas, A., Giannakopoulos, Y., Lazos, P. (2019). The Pareto Frontier of Inefficiency in Mechanism Design. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_14

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  • DOI: https://doi.org/10.1007/978-3-030-35389-6_14

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  • Online ISBN: 978-3-030-35389-6

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