Revelation strategies in all-pay auctions with an uncertain number of bidders

This paper discusses whether and how the auctioneer should reveal his private information about the numbers of bidders in all-pay auctions with independent-private valuations. We find that if there are at least two bidders then making bidders realize the existence of at least one rival is good for the auctioneer. Further, under the assumption that bidders' valuations are uniformly distributed, we investigate the optimal revelation strategies of the auctioneer who seeks to maximize total expected bids and the highest expected bid, respectively. The conclusions show that the optimal revelation strategies rely on the actual numbers of bidders. To maximize the highest expected bid, the auctioneer should reveal more accurate information.