MINIMIZING THE PROBABILITY OF A TIE FOR FIRST PLACE

Suppose that the scores of k players are independent integer valued ra ndom variables with probabilities p(j), j = 1,2,...,n. We investigate the distributions which minimize the probability of a tie for the high est score and show that these satisfy the limit law lim(n-->infinity)S igma(j less than or equal to nxPj) = x(2/k) for 0 less than or equal t o x less than or equal to 1. (C) 1996 Academic Press, Inc.