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Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated items and each item may have multiple units. Although the ascending auction is known to find an equilibrium price vector in finite time, little is known about its time complexity. The main aim of this paper is to analyze the time complexity of the ascending auction globally and locally, by utilizing the theory of discrete convex analysis. An exact bound on the number of iterations is given in terms of the ℓ ∞  distance between the initial price vector and an equilibrium, and an efficient algorithm to update a price vector is designedbased on a min-max theorem for submodular function minimization.

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Author information

Authors and Affiliations

  1. University of Tokyo, Tokyo, 113-8656, Japan

    Kazuo Murota

  2. Tohoku University, Sendai, 980-8579, Japan

    Akiyoshi Shioura

  3. University of York, York, YO10 5DD, UK

    Zaifu Yang

Authors
  1. Kazuo Murota
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  2. Akiyoshi Shioura
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  3. Zaifu Yang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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© 2013 Springer-Verlag Berlin Heidelberg

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Murota, K., Shioura, A., Yang, Z. (2013). Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_44

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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