  Static reduction of dynamic stochastic team problems has been an effective
method for establishing existence and approximation results for optimal
policies, as we have discussed extensively in Part I of this paper. In this
Part II of the two-part paper, we address stochastic dynamic games. Similar to
Part I, we consider two distinct types of static reductions: (i) those that are
policy-independent (as those introduced by Witsenhausen for teams), and (ii)
those that are policy-dependent (as those introduced by Ho and Chu for
partially nested dynamic teams). For the first type, aligned with the results
for teams in Part I, we first show that there is a bijection between Nash
equilibrium policies and their policy-independent static reductions. However,
for the second type, we show that the results of Part I on teams no longer hold
for Nash equilibria of dynamic nonzero-sum games. Sufficient conditions on the
cost functions are introduced to establish an equivalence relationship between
Nash equilibria of dynamic nonzero-sum games and their policy-dependent static
reductions. For zero-sum games, sufficient conditions are relaxed and stronger
results are established by exploiting the ordered interchangeability property
of multiple saddle points.
