Bray Theory Workshop
Resale gives rise to a kind of winner's curse in auctions even with independent private values (IPV), as an increase in one's bid may forego the gain of trade with the rival who would have been the reseller had it not been the increase. This winner's curse renders speculation possible that obscures bidders' information and presents a challenge to existing methods of proving existence of equilibrium in various auctions. This paper considers an asymmetric n-bidder IPV auction with resale, with the initial auction ranging from first-price to all-pay and the set of available resale mechanisms consisting of either all possible game forms or Vickrey and English auctions with reserves. It is proved that any monotone equilibrium in the auction-resale game has a no-atom property, so that all but one consequential bid fully reflect the bidder's private valuation. It is also proved that such an equilibrium exists for first-price auctions given any reserve price and for all-pay auction with zero reserve.