Abstract
AbstractWe study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders' types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in the second‐price and the English auctions. We establish there is no equivalence between these two auction designs, neither in bidding strategies nor in expected revenue. This is because the presence or the absence of an increasing price clock affects signaling incentives differently in both auction formats, and thereby also the bidders' incentives to overbid their types. This leads to a strictly higher expected revenue in the second‐price auction than in the English auction. Our analysis is completed by a comparison with other disclosure policies. Applications include art auctions and charity auctions.
Highlights
Signaling constitutes an important motivation and determinant for many forms of publicly observable behavior of individuals and organizations
The receiver’s inferences about the winning and losing bidders only depend on the winner’s bid, and not on the second highest bid. This means that the presence of a price clock does not play the role that it does in the English auction in which the payment is revealed, i.e., to constrain the bidder’s expectations of the receiver’s beliefs about the losing bidders, which causes the divergence in expected revenue between the second-price and the English auction if the winner’s payment is revealed to the receiver
We have studied the second-price and the English “button” auction with signaling, assuming that all bidders care about an outside observer’s beliefs about their type, if the outside observer sees the identity and payment of the auction’s winner
Summary
Signaling constitutes an important motivation and determinant for many forms of publicly observable behavior of individuals and organizations. In a fully separating equilibrium, the winner’s payment imposes a lower bound on the receiver’s beliefs about the winner’s type in the second-price auction and button auction This will be shown to induce the lowest types in both auctions to bid strictly above their value in equilibrium and can induce the highest types to bid strictly more than in the case without signaling. Haile (2003) examines how bidders’ incentives for signaling their type in function of a resale auction, in which the winner can resell the item to a loser, depend on the auction formats and information assumptions He shows that the revenue equivalence may not hold. Assuming as Goeree (2003) only the winning bidder is affected by the receiver’s inference, Liu (2012) analyzes takeovers through an ascending auction, and shows how the winner’s bidding strategy can signal the firm’s post-takeover value to the market.
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