Testing for and selecting strong players in a tournament

In this thesis we derive some testing and selection procedures for a tournament involving a set of n players that has two complimentary subsets of players, each consisting of approximately equally matched players. The background to this work is found in the work of Narayana and Zidek who, in Contributions to the theory of tournaments, II [8] considered the case involving one strong player with n-1 equally matched, weaker opponents. Their results are extended in this paper to include the possibility of k, 1 ≤ k ≤n, strong players. Moreover, we supply results which prove several of the unproved assertions in [8]. It becomes apparent that, the larger k is, the more restrictive the design must be and, also, the more inadequate the selection procedure is. Although no numerical and computational work has been done, asymptotic results have been obtained which are easily adapted for such purposes.Science, Faculty ofMathematics, Department ofGraduat