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Auctions with an Invitation Cost

Author

Listed:
  • Erik Ekström

    (Department of Mathematics, Uppsala University, Box 256, 75105 Uppsala, Sweden)

  • Carl Lindberg

    (Sigmastocks A3, Södra Hamngatan 19–21, 41114 Göteburg, Sweden)

Abstract

We consider an auction in which a seller invites potential buyers to a sealed-bid first-price auction, without disclosing to the buyers the number of extended invitations. In the presence of a fixed invitation cost for each invited bidder, the whole auction can be described as a game, where the set of players consists of all bidders together with the seller. In a setting with fully observable common values we show the existence of a Nash equilibrium in mixed strategies. In this equilibrium, the seller should invite precisely one or two potential buyers with certain probabilities, and each invited buyer should place a randomized bid according to a certain distribution.

Suggested Citation

  • Erik Ekström & Carl Lindberg, 2021. "Auctions with an Invitation Cost," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-16, March.
  • Handle: RePEc:wsi:igtrxx:v:23:y:2021:i:01:n:s0219198920500140
    DOI: 10.1142/S0219198920500140
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