  We study a general class of dynamic games with asymmetric information where
agents' beliefs are strategy dependent, i.e. signaling occurs. We show that the
notion of sufficient information, introduced in the companion paper team, can
be used to effectively compress the agents' information in a mutually
consistent manner that is sufficient for decision-making purposes. We present
instances of dynamic games with asymmetric information where we can
characterize a time-invariant information state for each agent. Based on the
notion of sufficient information, we define a class of equilibria for dynamic
games called Sufficient Information Based Perfect Bayesian Equilibrium
(SIB-PBE). Utilizing the notion of SIB-PBE, we provide a sequential
decomposition of dynamic games with asymmetric information over time; this
decomposition leads to a dynamic program that determines SIB-PBE of dynamic
games. Furthermore, we provide conditions under which we can guarantee the
existence of SIB-PBE.
