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Optimal Allocation in Combinatorial Auctions with Quadratic Utility Functions

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Theory and Applications of Models of Computation (TAMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6648))

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Abstract

We discuss the optimal allocation problem in combinatorial auction, where the items are allocated to bidders so that the sum of the bidders’ utilities is maximized. In this paper, we consider the case where utility functions are given by quadratic functions; the class of quadratic utility functions has a succinct representation but is sufficiently general. The main aim of this paper is to show the computational complexity of the optimal allocation problem with quadratic utility functions. We consider the cases where utility functions are submodular and supermodular, and show NP-hardness and/or polynomial-time exact/approximation algorithm. These results are given by using the relationship with graph cut problems such as the min/max cut problem and the multiway cut problem.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Akiyoshi Shioura & Shunya Suzuki

Authors
  1. Akiyoshi Shioura
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  2. Shunya Suzuki
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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Shioura, A., Suzuki, S. (2011). Optimal Allocation in Combinatorial Auctions with Quadratic Utility Functions. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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