  Parrondo's paradox is extended to regime switching random walks in random
environments. The paradoxical behavior of the resulting random walk is
explained by the effect of the random environment. Full characterization of the
asymptotic behavior is achieved in terms of the dimensions of some random
subspaces occurring in Oseledec's theorem. The regime switching mechanism gives
our models a richer and more complex asymptotic behavior than the simple random
walks in random environments appearing in the literature, in terms of
transience and recurrence.
