An optimal strategy for a conflict resolution problem

Abstract

Relevant to the design of multiple access protocols is the problem of finding the largest of N i.i.d. numbers X 1,…, X N uniformly distributed over [0,1] using the minimum number of questions of the following type. We pick a set A(1) ⊂ [0, 1] and ask which X i ϵ A(1). Depending on the response, we pick another subset A(2) and ask which X i ϵ A(2), and so on, until we identify the largest X i . It is shown that the optimum sequence of questions must be of the type A( k) = ( a( k), 1]; the best sequence { a( k)} can then be determined by dynamic programming following the work of Arrow, Pesotchinsky and Sobel.