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Black-Box Reductions in Mechanism Design

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2011, RANDOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6845))

Abstract

A central question in algorithmic mechanism design is to understand the additional difficulty introduced by truthfulness requirements in the design of approximation algorithms for social welfare maximization. In this paper, by studying the problem of single-parameter combinatorial auctions, we obtain the first black-box reduction that converts any approximation algorithm to a truthful mechanism with essentially the same approximation factor in a prior-free setting. In fact, our reduction works for the more general class of symmetric single-parameter problems. Here, a problem is symmetric if its allocation space is closed under permutations.

As extensions, we also take an initial step towards exploring the power of black-box reductions for general single-parameter and multi-parameter problems by showing several positive and negative results. We believe that the algorithmic and game theoretic insights gained from our approach will help better understand the tradeoff between approximability and the incentive compatibility.

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Author information

Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, PA, 19104, USA

    Zhiyi Huang

  2. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Lei Wang

  3. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Yuan Zhou

Authors
  1. Zhiyi Huang
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  2. Lei Wang
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  3. Yuan Zhou
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  2. Department of Computer Science, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA

    R. Ravi

  4. Centre Universitaire d’Informatique,, University of Geneva,, Battelle A 7 route de Drize, 1227, Carouge, Switzerland

    José D. P. Rolim

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© 2011 Springer-Verlag Berlin Heidelberg

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Huang, Z., Wang, L., Zhou, Y. (2011). Black-Box Reductions in Mechanism Design. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2011 2011. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22935-0_22

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  • DOI: https://doi.org/10.1007/978-3-642-22935-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22934-3

  • Online ISBN: 978-3-642-22935-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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