On the Value of Randomizing and Limiting Memory in Repeated Decision-Making under Minimal Regret

We search for behavioral rules that attain minimax regret under geometric discounting in the context of repeated decision making in a stationary environment where payo¤s belong to a given bounded interval. Rules that attain minimax regret exist and are optimal for Bayesian decision making under the prior where learning can be argued to be most di¢cult. Minimax regret can be attained by randomizing using a linear function of the previous payo¤s. For myopic individuals, minimax regret behavior requires only one round of memory, for intermediate discount factors two rounds of memory su¢ce to attain minimax regret. JEL classi...cation: D81, D83.