A Sealed-Bid Two-Attribute Yardstick Auction Without Prior Scoring


We analyze a two-attribute single item procurement auction that uses yardstick competition to settle prices. The auction simplifies the procurement process by reducing the principal’s articulation of preferences to simply choosing the most preferred offer as if it was a market with posted prices. This is done simply by replacing the submitted sealed bids by yardstick bids, computed by a linear weighting of the other participants’ bids. We show that there is only one type of Nash equilibria where some agents may win the auction by submitting a zero price-bid. Using a simulation study we demonstrate that following this type of equilibrium behavior often leads to winner’s curse. The simulations show that in auctions with more than 12 participants the chance of facing winner’s curse is around 95 %. Truthful reporting, on the other hand, does not constitute a Nash equilibrium but it is ex post individually rational. Using a simulation study we demonstrate that truthful bidding may indeed represent some kind of focal point.

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  1. 1.

    For instance think of a procurement decision in a cooperative where different members’ interests have to be aggregated

  2. 2.

    In a first score auction, the bidder with the highest score wins and has to meet the highest score. In a second score auction, the bidder with the highest score wins and has to meet the second highest score.

  3. 3.

    Using the revenue equivalence theorem as it is presented in Riley and Samuelson (1981).

  4. 4.

    However, it is not given that the second score auction is the most preferred auction by the principal. Bogetoft and Nielsen (2008) show that it is possible for the principal to extract more informational rent while the auction remains efficient and strategy-proof.

  5. 5.

    The idea of a yardstick auction can also be found in Aparicio et al. (2008). They suggest an auction design for so-called combinatorial auctions based on the same type of yardstick principle.

  6. 6.

    Note that if the other bidders were allowed a higher degree of misreporting our results will be even stronger in the sense that there will be even fewer cases where the auction is won with a gain.


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Correspondence to Kurt Nielsen.

Additional information

Financial support from the Center for research in the Foundations of Electronic Markets (CFEM), funded by the Danish Council for Strategic Research is gratefully acknowledged.

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Hougaard, J.L., Nielsen, K. & Papakonstantinou, A. A Sealed-Bid Two-Attribute Yardstick Auction Without Prior Scoring. Group Decis Negot 25, 827–843 (2016). https://doi.org/10.1007/s10726-015-9463-5

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  • Multi-attribute auctions
  • Yardstick competition
  • Articulation of preferences