Private-Value Auctions, Resale, and Common Value

We establish the bid-equivalence between an independent private-value (IPV) …rst-price auction model with resale and a model of …rst-price common-value auctions. The common value is de…ned by the transaction price when trade takes place. When there is no trade, the common value is de…ned through a monotonic extension of the resale price function. We show bid equivalence when (1) there are two bidders with a general resale mechanism; (2) there is one regular buyer and many speculators with a monopoly resale market; (3) there are two groups of identical bidders and the winning bidder in the resale stage conducts a second-price auction to sell the object to the losing bidders. The buyer-speculators model of auction with resale is bid-equivalent to the Wilson Drainage Tract common value model. We assume that the resale market satis…es a weak e¢ ciency property, which means that trade must be e¢ cient when the trade surplus is the highest possible under incomplete information. We show that when the weak e¢ ciency property fails, the bid equivalence result may fail. We want to thank Kalyan Chatterjee, Isa Hafalir, Vijay Krishna, Bernard Lebrun, Hao Li, Michael Schwarz, John Wooders, Lixin Ye and Charles Zheng for helpful comments. Financial assistance for visits to KIER, Kyoto University; ECARES, Belgium, and CAPOP, Penn State are gratefully acknowledged. Please contact Harrison Cheng at [email protected] and Guofu Tan at [email protected] for comments and further suggestions.