The tripartite auction folk theorem

Abstract

We formally study two bidder first-price, second-price, and all-pay auctions with known values, deriving the equilibrium payoffs and strategies and showing when all three yield the same equilibrium payoffs to the bidders. This latter result, the tripartite auction theorem, does not hold for all auctions, in particular it can fail for symmetric auctions with high stakes and in auctions with very low stakes.