  Two natural strategy elimination procedures have been studied for strategic
games. The first one involves the notion of (strict, weak, etc) dominance and
the second the notion of rationalizability. In the case of dominance the
criterion of order independence allowed us to clarify which notions and under
what circumstances are robust. In the case of rationalizability this criterion
has not been considered. In this paper we investigate the problem of order
independence for rationalizability by focusing on three naturally entailed
reduction relations on games. These reduction relations are distinguished by
the adopted reference point for the notion of a better response. Additionally,
they are parametrized by the adopted system of beliefs. We show that for one
reduction relation the outcome of its (possibly transfinite) iterations does
not depend on the order of elimination of the strategies. This result does not
hold for the other two reduction relations. However, under a natural assumption
the iterations of all three reduction relations yield the same outcome. The
obtained order independence results apply to the frameworks considered in
Bernheim 84 and Pearce 84. For finite games the iterations of all three
reduction relations coincide and the order independence holds for three natural
systems of beliefs considered in the literature.
