The minimax adjustment principle

The minimax adjustment principle presented in this paper uses the minimax principle in order to improve a given action in the light of some knowledge on the state of the nature or on the other actors. It turns out that the given action is kept unchanged if it can be reconciled with the external information, and otherwise, it is adjusted to the given knowledge in such a way that it remains as close as possible to the original action. The general approach is applied to two examples, the one comes from statistics, and the other is from economics. Here, the external information is represented by ellipsoidal sets.