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Approximately Optimal Auctions With a Strong Bidder

Author

Listed:
  • Luca Anderlini
  • GaOn Kim
Abstract
We consider auctions with N+1 bidders. Of these, N are symmetric and N+1 is "sufficiently strong" relative to the others. The auction is a "tournament" in which the first N players bid to win the right to compete with N+1. The bids of the first N players are binding and the highest bidder proceeds to a second-price competition with N+1. When N+1's values converge in distribution to an atom above the upper end of the distribution of the N bidders and the rest of the distribution is drained away from low values sufficiently slowly, the auction's expected revenue is arbitrarily close to the one obtained in a Myerson (1981) optimal auction. The tournament design is "detail free" in the sense that no specific knowledge of the distributions is needed in addition to the fact that bidder N+1 is stronger than the others as required. In particular, no additional information about the value of the atom is needed. This is important since mis-calibrating by a small amount an attempt to implement the optimal auction can lead to large losses in revenue. We provide an interpretation of these results as possibly providing guidelines to a seller on how to strategically "populate" auctions with a single bidder even when only weaker bidders are available.

Suggested Citation

  • Luca Anderlini & GaOn Kim, 2024. "Approximately Optimal Auctions With a Strong Bidder," Papers 2409.11048, arXiv.org.
    • Handle: RePEc:arx:papers:2409.11048
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    File URL: http://arxiv.org/pdf/2409.11048
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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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