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We study minimax regret treatment rules in finite samples under matched treatment assignment in a setup where a policymaker, informed by a sample, needs to decide between different 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 finite 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. We also discuss numerical approaches to approximate minimax regret rules for unbalanced samples. We then study minimax regret treatment rules in finite samples when a specific quantile (rather than expected outcome) is the object of interest. We establish that all treatment rules are minimax regret under ““matched”“ and ““random sampling”“ schemes while under ““testing an innovation”“ no-data rules are shown to be minimax regret.
