Existence of Equilibria in Procurement Auctions

This paper investigates symmetric equilibria in first- and second-price auctions with multidimensional types. The constructed model mirrors the information structure of actual procurement auctions. We demonstrate by a counterexample that symmetric and continuous type distribution is not a sufficient condition for the existence of a pure-strategy equilibrium, but it is guaranteed if distributions of all components are log-concave. We state a new Revenue Equivalence Theorem applied to first- and second-price auctions and conclude that the two standard auction formats yields the same expected price to the auctioneer.