Average-case interactive communication

X and Y are random variables. Person P/sub x/ knows X, Person P/sub y/ knows Y, and both know the joint probability distribution of the pair (X,Y). Using a predetermined protocol, they communicate over a binary error-free channel in order for P/sub y/ to learn X. P/sub x/ may or may not learn Y. It is determined how many information bits must be transmitted (by both persons) on the average. The results show that, when the arithmetic average number of bits is considered, there is no asymptotic advantage to P/sub x/ knowing Y in advance and four messages are asymptotically optimum. By contrast, for the worst-case number of bits, communication can be significantly reduced if P/sub x/ knows Y in advance, and it is not known whether a constant number of messages is asymptotically optimum.< >