  In this work, we study two models of arbitrarily varying channels, when
causal side information is available at the encoder in a causal manner. First,
we study the arbitrarily varying channel (AVC) with input and state
constraints, when the encoder has state information in a causal manner. Lower
and upper bounds on the random code capacity are developed. A lower bound on
the deterministic code capacity is established in the case of a
message-averaged input constraint. In the setting where a state constraint is
imposed on the jammer, while the user is under no constraints, the random code
bounds coincide, and the random code capacity is determined. Furthermore, for
this scenario, a generalized non-symmetrizability condition is stated, under
which the deterministic code capacity coincides with the random code capacity.
  A second model considered in our work is the arbitrarily varying degraded
broadcast channel with causal side information at the encoder (without
constraints). We establish inner and outer bounds on both the random code
capacity region and the deterministic code capacity region. The capacity region
is then determined for a class of channels satisfying a condition on the mutual
informations between the strategy variables and the channel outputs. As an
example, we show that the condition holds for the arbitrarily varying binary
symmetric broadcast channel, and we find the corresponding capacity region.
