In this paper, we consider finite normal form games satisfying transference of decisionmaker indifference. We show that any set of strategies surviving k rounds of elimination of some weakly dominated strategies can be reduced to a set of strategies equivalent to the set of strategies surviving k rounds of elimination of all weakly dominated strategies in every round by (at most k) further rounds of elimination of weakly dominated strategies. The result develops work by Gretlein (Dominance Elimination Procedures on Finite Alternative Games, Int J Game Theory 12, 107-113, 1983). We then consider applications and demonstrate how we may obtain a unified approach to the above mentioned work by Gretlein and recent work by Ewerhart (Iterated Weak Dominance in Strictly Competitive Games of Perfect Information, J Econ Theory 107, 474-482, 2002) and Marx and Swinkels (Order Independence for Iterated Weak Dominance, Games Econ Behav 18, 219-245, 1997).
