Sealed Bid Multi-object Auctions with Necessary Bundles and its Application to Spectrum Auctions

  • Tomomi Matsui
  • Takahiro Watanabe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2132)


In this paper, we consider multi-object auctions in which each bidder has a positive reservation value for only one special subset of objects, called a necessary bundle. In the auction, each bidder reports its necessary bundle and its reservation value. The seller solves the assignment problem of objects which maximizes its revenue and decides the winning bidders who can purchase their necessary bundles for their reporting prices. We show that this auction leads to an efficient allocation through Nash equilibria under complete information when the bid-grid size is sufficiently small. We apply our results to spectrum auctions satisfying the conditions that necessary bundles are intervals of discretized radio spectrum. We show that the revenue maximization problem for the seller can be solved in polynomial time for the above auctions. The algorithm also indicates a method to choose an accepted bidder randomly when the revenue maximization problem has multiple optimal solutions. Lastly, we introduce a linear inequality system which characterizes the set of Nash equilibria.


Nash Equilibrium Combinatorial Auction Walrasian Equilibrium Pure Strategy Nash Equilibrium Auction Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tomomi Matsui
    • 1
  • Takahiro Watanabe
    • 2
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan
  2. 2.Department of Policy StudiesIwate Prefectural UniversityUSA

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