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Bidding in Common‐Value Auctions With an Unknown Number of Competitors

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  • Stephan Lauermann
  • Andre Speit

Abstract

This paper studies a first‐price common‐value auction in which bidders do not know the number of their competitors. In contrast to the case of common‐value auctions with a known number of rival bidders, the inference from winning is not monotone, and a “winner's blessing” emerges at low bids. As a result, bidding strategies may not be strictly increasing, but instead may contain atoms. Moreover, an equilibrium fails to exist when the expected number of competitors is large and the bid space is continuous. Therefore, we consider auctions on a grid. On a fine grid, high‐signal bidders follow an essentially strictly increasing strategy, whereas low‐signal bidders pool on two adjacent bids on the grid. The solutions of a “communication extension” based on Jackson, Simon, Swinkels, and Zame (2002) capture the equilibrium bidding behavior in the limit, as the grid becomes arbitrarily fine.

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  • Stephan Lauermann & Andre Speit, 2023. "Bidding in Common‐Value Auctions With an Unknown Number of Competitors," Econometrica, Econometric Society, vol. 91(2), pages 493-527, March.
    • Handle: RePEc:wly:emetrp:v:91:y:2023:i:2:p:493-527
    DOI: 10.3982/ECTA17793
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    References listed on IDEAS

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    7. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
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    10. Stephan Lauermann & Andre Speit, 2019. "Bidding in Common-Value Auctions With an Uncertain Number of Competitors," CRC TR 224 Discussion Paper Series crctr224_2019_136, University of Bonn and University of Mannheim, Germany.
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    1. Francesco De Sinopoli & Leo Ferraris & Claudia Meroni, 2024. "Group size as selection device," Working Papers 533, University of Milano-Bicocca, Department of Economics.

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