Simultaneous Single-Item Auctions

  • Kshipra Bhawalkar
  • Tim Roughgarden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)


In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via single-item auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying single-item auction. We provide a thorough understanding of the price of anarchy, as a function of the single-item auction payment rule.

When the payment rule depends on the winner’s bid, as in a first-price auction, we characterize the worst-case price of anarchy in the corresponding CAs with item bidding in terms of a sensitivity measure of the payment rule. As a corollary, we show that equilibrium existence guarantees broader than that of the first-price rule can only be achieved by sacrificing its property of having only fully efficient (pure) Nash equilibria.

For payment rules that are independent of the winner’s bid, we prove a strong optimality result for the canonical second-price auction. First, its set of pure Nash equilibria is always a superset of that of every other payment rule. Despite this, its worst-case POA is no worse than that of any other payment rule that is independent of the winner’s bid.


Nash Equilibrium Combinatorial Auction Price Rule Equilibrium Allocation Pure Nash Equilibrium 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kshipra Bhawalkar
    • 1
  • Tim Roughgarden
    • 1
  1. 1.Stanford UniversityStanfordUSA

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