Introduction These notes essentially tie up a few loose ends in Lecture 8; in particular, I exhibit examples of inefficiencies in first- and second-price auctions. I would also like to briefly comment on Questions 1 and 2 in Problem Set 2 The first-price auction may be inefficient even with private values Both examples I am going to show are due to Eric Maskin(to the best of my knowledge) The first point I wish to make is that, even in a private-values setting, asymmetries may
Player i is rational\;R=nieN Ri. Also, Bi(E) is the event \Player i is certain that E is true\ and B(E)=neN Bi(E). This is as in Lecture 7. Let me introduce the following notation for iterated mutual certainty: B()(E)=E B()(E)=B(B-I)(E)). Then the definition of Bk in Lecture 7 can be rewritten as Bk