A natural question to ask next is whether iterated strict
dominance remains computationally easy when dominating
strategies are required to place positive probability on at
most k pure strategies, where k is a small constant. (We
have already shown in Section 4 that iterated weak dominance
is hard even when k = 1, that is, only dominance by
pure strategies is allowed.) Of course, if iterated strict dominance
were path-independent under this restriction, computational
easiness would follow as it did in Section 4. However,
it turns out that this is not the case.