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Distributed Algorithmic Mechanism Design and Algebraic Communication Complexity

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Algorithmic Game Theory (SAGT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4997))

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Abstract

In this paper, we introduce and develop the field of algebraic communication complexity, the theory dealing with the least number of messages to be exchanged between two players in order to compute the value of a polynomial or rational function depending on an input distributed between the two players. We define a general algebraic model, where the involved functions can be computed with the natural operations additions, multiplications and divisions and possibly with comparisons. We provide various lower bound techniques, mainly for fields of characteristic 0.

We then apply this general theory to problems from distributed mechanism design, in particular to the multicast cost sharing problem, and study the number of messages that need to be exchanged to compute the outcome of the mechanism. This addresses a question raised by Feigenbaum, Papadimitriou, and Shenker [9].

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Author information

Authors and Affiliations

  1. Computer Science, Saarland University, Postfach 151150, 66041, Saarbrücken, Germany

    Markus Bläser

  2. Institute of Theoretical Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Elias Vicari

Authors
  1. Markus Bläser
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  2. Elias Vicari
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Burkhard Monien  & Ulf-Peter Schroeder  & 

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Bläser, M., Vicari, E. (2008). Distributed Algorithmic Mechanism Design and Algebraic Communication Complexity. In: Monien, B., Schroeder, UP. (eds) Algorithmic Game Theory. SAGT 2008. Lecture Notes in Computer Science, vol 4997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79309-0_19

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  • DOI: https://doi.org/10.1007/978-3-540-79309-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79308-3

  • Online ISBN: 978-3-540-79309-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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