Information Asymmetries in Common-Value Auctions with Discrete Signals

We consider common-value hybrid auctions among two asymmetrically informed bidders, where the winning bidder pays his bid with some positive probability k and the losing bid otherwise. Under the assumption of discrete and affiliated signals, we give an explicit characterization of the (unique) equilibrium, based on a simple recurrence relation, which gives rise to a linear-time algorithm for explicitly computing the equilibrium. By analyzing the execution of the algorithm, we derive several insights about the equilibrium structure. First, we show that equilibrium revenue is decreasing in k, and that the limit second-price equilibrium selected as k->0 has highest revenue, in stark contrast to the revenue collapse of the second-price auction predicted by the trembling-hand equilibrium selection of Abraham et al. We further show that the Linkage Principle can fail to hold even in a pure first-price auction with binary signals: public revelation of a signal to both bidders may decrease the auctioneer's revenue. Lastly, we analyze the effects of public acquisition of additional information on bidder utilities and exhibit cases in which both bidders strictly prefer for a specific bidder to receive additional information.