In this communication we examine the relationship between maxi–min, Bayes and Nash designs for some hypothesis testing problems. In particular we consider the problem of sample allocation in the standard analysis of variance framework and show that the maxi–min design is also a Bayes solution with respect to the least favourable prior, as well as a solution to a game theoretic problem, which we refer to as a Nash design. In addition, an extension to tests for order is provided.
"On Bayes and Nash experimental designs for hypothesis testing problems." Electron. J. Statist. 14 (2) 3976 - 4003, 2020. https://doi.org/10.1214/20-EJS1763