Nested removal of strictly dominated strategies in infinite games

We compare two procedures for the iterated removal of strictly dominated strategies. In the nested procedure, a strategy of a player is removed only if it is dominated by an unremoved strategy. The universal procedure is more comprehensive for it allows the removal of strategies that are dominated by previously removed ones. Outside the class of finite games, the two procedures may lead to different outcomes in that the universal one is always order independent while the other is not. We provide necessary and sufficient conditions for the equivalence of the two procedures. The conditions we give are based on completely bounded subsets of strategy profiles, which are variations of the bounded mechanisms from the literature on full implementation. The two elimination procedures are also shown to be equivalent in quasisupermodular games as well as in games with compact strategy spaces and upper semicontinuous payoff functions. Finally, we give an example of a game in which the nested procedure is order independent but not equivalent to the universal one, thus showing that order independence is not sufficient to guarantee the equivalence of the two elimination procedures.