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Truthful Mechanisms via Greedy Iterative Packing

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

An important research thread in algorithmic game theory studies the design of efficient truthful mechanisms that approximate the optimal social welfare. A fundamental question is whether an α-approximation algorithm translates into an α-approximate truthful mechanism. It is well-known that plugging an α-approximation algorithm into the VCG technique may not yield a truthful mechanism. Thus, it is natural to investigate properties of approximation algorithms that enable their use in truthful mechanisms.

The main contribution of this paper is to identify a useful and natural property of approximation algorithms, which we call loser-independence; this property is applicable in the single-minded and single-parameter settings. Intuitively, a loser-independent algorithm does not change its outcome when the bid of a losing agent increases, unless that agent becomes a winner. We demonstrate that loser-independent algorithms can be employed as sub-procedures in a greedy iterative packing approach while preserving monotonicity. A greedy iterative approach provides a good approximation in the context of maximizing a non-decreasing submodular function subject to independence constraints. Our framework gives rise to truthful approximation mechanisms for various problems. Notably, some problems arise in online mechanism design.

Proofs and details omitted from this extended abstract appear in the full version of this paper. The first author was partially supported by NSF grants CCF-0728782 and CNS-0721899. The second author was supported by the Binational Science Foundation, by the Israel Science Foundation, by the European Commission under the Integrated Project QAP funded by the IST directorate as Contract Number 015848, and by a European Research Council (ERC) Starting Grant.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois, Urbana, IL, 61801, USA

    Chandra Chekuri

  2. Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Iftah Gamzu

Authors
  1. Chandra Chekuri
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  2. Iftah Gamzu
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Editor information

Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

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

    José Rolim

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Chekuri, C., Gamzu, I. (2009). Truthful Mechanisms via Greedy Iterative Packing. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

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