Bayesian Combinatorial Auctions

  • George Christodoulou
  • Annamária Kovács
  • Michael Schapira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)


We study the following Bayesian setting: m items are sold to n selfish bidders in m independent second-price auctions. Each bidder has a private valuation function that expresses complex preferences over all subsets of items. Bidders only have beliefs about the valuation functions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular valuation functions, then every Bayesian Nash equilibrium of the resulting game provides a 2-approximation to the optimal social welfare. Moreover, we show that in the full-information game a pure Nash always exists and can be found in time that is polynomial in both m and n.


Nash Equilibrium Polynomial Time Valuation Function Additive Valuation Combinatorial Auction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • George Christodoulou
    • 1
  • Annamária Kovács
    • 2
  • Michael Schapira
    • 3
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Institute for Computer ScienceJ. W. Goethe UniversityFrankfurt/MainGermany
  3. 3.The School of Computer Science and EngineeringThe Hebrew University of JerusalemIsrael

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