A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are “erroneous” in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. Such passive errors...

Maskin and Riley (2003) and Lebrun (2006) prove that the Bayes-Nash equilibrium of �rst-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric �rst-price auctions (with or without a minimum bid), the...

As a selling mechanism, auctions have acquired a central position in the free market economy all over the globe. This development has deepened, broadened, and expanded the theory of auctions in new directions. This chapter is intended as a selective update of some of the developments and...