Second-price common-value auctions under multidimensional uncertainty

The literature has demonstrated that second-price common-value auctions are sensitive to the presence of asymmetries among bidders. Bikhchandani (1988) has shown that if it is common knowledge that a bidder has a disadvantage compared to her opponent, this bidder (almost surely) never wins the auction. This paper is the first to show that this result does not carry through when one allows for two-sided uncertainty. Whe show that even if the probabilities that one of the bidders is advantaged while the other one is disadvantaged are arbitrarily large, in every equilibrium, the disadvantaged bidder needs to win the auction with strictly positive probability. We then solve for the equilibria in two cases (one with two types and another with a continuum of types) and we characterize their expected revenues properties. We find that although they underperform relative to "comparable" symmetric auctions, they perform much better than what it is "assumed" in the literature.