We consider parametric examples of two-bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent’s private valuation. In such multidimensional private value auction environments, we show that the revenue equivalence between the ﬁrst and second price auctions breaks down and there is no deﬁnite revenue ranking; while the second price auction is always eﬀicient allocatively, the ﬁrst price auction may be ineﬀicient and the ineﬀiciency may increase as the signal becomes more informative; equilibria may fail to exist for the ﬁrst price auction. We also show that auction mechanisms provide diﬀerent incentives for bidders to acquire costly information about opponents’ valuation.
Fang, Hanming and Morris, Stephen, "Multidimensional Private Value Auctions" (2003). Cowles Foundation Discussion Papers. 1693.