Assaf, David; Samuel-Cahn, Ester - Center for the Study of Rationality, Hebrew University … - 2003
Let X_i be nonnegative independent random variables with finite expectations and X^*_n = max {X_1, ..., X_n}. The value EX^*_n is what can be obtained by a ``prophet". A ``mortal" on the other hand, may use k = 1 stopping rules t_1, ..., t_k yielding a return E[max_{i=1, ..., k} X_{t_i}]. For n...