Worst‐case equilibria in first‐price auctions

Abstract

The usual analysis of bidding in first‐price auctions assumes that bidders know the distribution of valuations. We analyze first‐price auctions in which bidders do not know the precise distribution of their competitors' valuations, but only the mean of the distribution. We propose a novel equilibrium solution concept based on worst‐case reasoning. We find an essentially unique and efficient worst‐case equilibrium of the first‐price auction that has appealing properties from both the bidders' and the seller's point of view.