Reserve price signaling in first-price auctions with an uncertain number of bidders
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Reserve price signaling in first‑price auctions with an uncertain number of bidders Toshihiro Tsuchihashi1 Accepted: 16 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We study first-price auctions in which the number of bidders is the seller’s private information, and investigate the use of a reserve price to signal this private information. We use the D1 criterion to refine the set of equilibria and characterize a symmetric separating equilibrium outcome, where the reserve price increases with the number of bidders. The key driving force is a certain form of single-crossing property. With more bidders, the seller can afford a high reserve price that discourages competition in the auction, for the winning bid is more likely to be higher. Keywords First-price auctions · Uncertain number of bidders · Signaling games · Reserve price signaling
1 Introduction In an auction, the seller and the bidders often have asymmetric information. For example, the valuation of the auctioned object is clearly a source of asymmetric information. Furthermore, although it is frequently ignored in the literature, the number of bidders can also be a source of asymmetric information. Bidders are likely uninformed about the number of competitors in an auction, whereas the seller may have this information. Examples in which the number of bidders is a source of asymmetric
I am truly indebted to the attendees of the Sapporo Workshop on Industrial Economics at Sapporo Gakuin University, the MicroLab at Universitat Autònoma de Barcelona, and the JEI2018 at Universitat de Barcelona for their helpful comments and suggestions and invaluable guidance. Any remaining errors are, of course, my own responsibility. * Toshihiro Tsuchihashi [email protected] 1
Faculty of Economics, Daito Bunka University, Tokyo 175‑8571, Japan
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information include designated procurement auctions and online auctions.1 For designated procurement auctions, the government selects participants, and the identities of these participants are the government’s private information.2 Thus, the participants in such an auction cannot identify their competitors. In the case of online auctions, a potential bidder can add favorable auctions to his watch list, so the seller privately holds information about the number of bidders watching her auction.3 Once a seller finds a substantial number of bidders to participate in her auction, she may want to disclose the number of bidders. This disclosure seems natural, especially for first-price auctions (FPAs), because bidding competition intensifies as the number of bidders increases. However, the seller needs a device to credibly transmit this information to bidders; otherwise, a strategic incentive emerges.4 Specifically, if the bidders are naive to the seller’s disclosure, she will have an incentive to manipulate their beliefs. In this study, we investigate the use of a reserve price to signal the number of bidders.5 If a seller chooses a reserve price a
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