2 - Private value auctions: A first look

Abstract

This chapter introduces the basic methodology of auction theory. The relative performance of the auction formats on grounds of revenue or efficiency is evaluated by comparing the equilibrium outcomes in one format versus another. Under a first-price sealed-bid auction, the highest bidder gets the object and pays the amount he bid. Under second-price sealed-bid auction, the highest bidder gets the object and pays the second highest bid. The strategic problem confronting bidders in second-price auctions is much simpler than that in first-price auctions, so they constitute a natural starting point. Also recall that in the private values framework, second-price auctions are equivalent to open ascending price auctions. In a first-price auction, equilibrium behavior is more complicated than in a second-price auction. Clearly, no bidder would bid an amount equal to his or her value as this would only guarantee a payoff of zero. In this case, the equilibrium strategy calls upon a bidder to bid a constant fraction of his value.