  Problems dealing with the ability to take an action that affects the states
of state-dependent communication channels are of timely interest and
importance. Therefore, we extend the study of action-dependent channels, which
until now focused on point-to-point models, to multiple-access channels (MAC).
In this paper, we consider a two-user, state-dependent MAC, in which one of the
encoders, called the informed encoder, is allowed to take an action that
affects the formation of the channel states. Two independent messages are to be
sent through the channel: a common message known to both encoders and a private
message known only to the informed encoder. In addition, the informed encoder
has access to the sequence of channel states in a non-causal manner. Our
framework generalizes previously evaluated settings of state dependent
point-to-point channels with actions and MACs with common messages. We derive a
single letter characterization of the capacity region for this setting. Using
this general result, we obtain and compute the capacity region for the Gaussian
action-dependent MAC. The unique methods used in solving the Gaussian case are
then applied to obtain the capacity of the Gaussian action-dependent
point-to-point channel; a problem was left open until this work. Finally, we
establish some dualities between action-dependent channel coding and source
coding problems. Specifically, we obtain a duality between the considered MAC
setting and the rate distortion model known as "Successive Refinement with
Actions". This is done by developing a set of simple duality principles that
enable us to successfully evaluate the outcome of one problem given the other.
