This paper deals with the computational complexity of some yes/no prob
lems associated with sequential elimination of strategies using three
domination relations: strong domination (strict inequalities), weak do
mination (weak inequalities), and domination (the asymmetric part of w
eak domination). Classification of various problems as polynomial or N
P-complete seems to suggest that strong domination is a simple notion,
whereas weak domination and domination are complicated ones.