Iterated Bounded Dominance

Based on the desideratum of undominated dominators (Jackson 1992), we provide a notion of iterated elimination of boundedly dominated strategies for a general class of strategic games and a wide variety of dominance relations. By introducing forgetfulness-proof games, we establish an equivalence result between the usual iterated dominance, our notion of iterated bounded dominance, and Gilboa et al.'s (1990) procedure requiring uneliminated dominators