The efficiency of subset selection of an epsilon-best uniform population relative to selection of the best one

Assume k (\geq 2) uniform populations are given on (\mu_i - ½, \mu_i + ½) with location parameter \mu_i \in R^1, i = 1, ..., k. The best population is defined as the population with the largest value of the location parameter. In \epsilon-best population (with \epsilon \geq 0) is a population with location parameter on a distance not larger than \epsilon from the largest value of \mu. It is possible to consider subset selection for an \epsilon-best population relative to subset selection for the best one. The relative efficiency is defined and computed in dependence of k and \epsilon for some values of the confidence level P* of selection