  For sequential stochastic control problems with standard Borel measurement
and control action spaces, we introduce a general (universally applicable)
dynamic programming formulation, establish its well-posedness, and provide new
existence results for optimal policies. Our dynamic program builds in part on
Witsenhausen's standard form, but with a different formulation for the state,
action, and transition dynamics. Using recent results on measurability
properties of strategic measures in decentralized control, we obtain a standard
Borel controlled Markov model. This allows for a well-defined dynamic
programming recursion through universal measurability properties of the value
functions for each time stage. In addition, new existence results are obtained
for optimal policies in decentralized stochastic control. These state that for
a static team with independent measurements, it suffices for the cost function
to be continuous (only) in the actions for the existence of an optimal policy
under mild compactness (or tightness) conditions. These also apply to dynamic
teams which admit static reductions with independent measurements through a
change of measure transformation. We show through a counterexample that weaker
conditions may not lead to existence of an optimal team policy. The paper's
existence results generalize those previously reported in the literature. A
summary of and comparison with previously reported results and some
applications are presented.
