New results on minimax regret treatment rules in finite samples

Abstract
We study minimax regret treatment rules in …nite samples under matched treatment
assignment in a setup where a policymaker, informed by a sample, needs to decide
between T di¤erent treatments for a T  2. Randomized rules are allowed for. We
show that the generalization of the minimax regret rule derived in Stoye (2009) for
the case T = 2 is minimax regret for general …nite T > 2. We also show by example,
that in the case of random assignment the generalization of the minimax rule in Stoye
(2009) to the case T > 2 is not necessarily minimax regret and derive minimax regret
rules for a few small sample cases, e.g. for N = 2 when T = 3:
In the case where a covariate x is included, it is shown that a minimax regret rule is
obtained by using minimax regret rules in the "conditional-on-x" problem if the latter
are obtained as Nash equilibria.