We study how the outcomes of a private-value ﬁrst price auction can vary with bidders’ information, for a ﬁxed distribution of private values. In a two bidder, two value, setting, we characterize all combinations of bidder surplus and revenue that can arise, and identify the information structure that minimizes revenue. The extremal information structure that minimizes revenue entails each bidder observing a noisy and correlated signal about the other bidder’s value. In the general environment with many bidders and many values, we characterize the minimum bidder surplus of each bidder and maximum revenue across all information structures. The extremal information structure that simultaneously attains these bounds entails an eﬀicient allocation, bidders knowing whether they will win or lose, losers bidding their true value and winners being induced to bid high by partial information about the highest losing bid. Our analysis uses a linear algebraic characterization of equilibria across all information structures, and we report simulations of properties of the set of all equilibria.
Bergemann, Dirk; Brooks, Benjamin; and Morris, Stephen, "Extremal Information Structures in the First Price Auction" (2013). Cowles Foundation Discussion Papers. 2319.