  The literature on evolutionary game theory suggests that pure strategies that
are strictly dominated by other pure strategies always become extinct under
imitative game dynamics, but they can survive under innovative dynamics. As we
explain, this is because innovative dynamics favour rare strategies while
standard imitative dynamics do not. However, as we also show, there are
reasonable imitation protocols that favour rare or frequent strategies, thus
allowing strictly dominated strategies to survive in large classes of imitation
dynamics. Dominated strategies can persist at nontrivial frequencies even when
the level of domination is not small.
