Root dominance is an intermediate dominance relation between weak and strict dominances. In addition to weak dominance, root dominance requires strict dominance on all profiles where an opponent plays a best response to the dominating strategy. The iterated elimination of root dominated strategies (IERDS) outcome refines the iterated elimination of strictly dominated strategies (IESDS) outcome, and IERDS is an order independent procedure in finite games, contrary to the iterated elimination of weakly dominated strategies (IEWDS). In addition, IERDS does not face the inconsistency that we call mutability. That is, IERDS does not alter the dominance relation between two strategies like IEWDS does. Finally, we introduce a rationality concept which corresponds to root undominated strategies. This rationality concept is induced by perturbations of the game such that a player believes that the strategies he considers might be observable by his opponent. We discuss the links between our concept and other concepts established in various literatures such as the conjectural variations theory.
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