Optimal designs for testing pairwise differences: A graph-based game theoretic approach

In a variety of experimental settings there is an interest in comparing pairs–of–treatments. Such experiments usually address one of the following two scientific questions: (1) is there a difference within any of the selected pairs of treatments? or (2) is there a difference within all of the selected pairs of treatments? In this article, we propose max–min optimal designs for testing the above hypotheses using a graph-based game theoretic approach. Some of the max–min designs obtained are well known, but not recognized as optimal, others are novel and provide an improvement over naive designs.