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