  Action-dependent channels model scenarios in which transmission takes place
in two successive phases. In the first phase, the encoder selects an "action"
sequence, with the twofold aim of conveying information to the receiver and of
affecting in a desired way the state of the channel to be used in the second
phase. In the second phase, communication takes place in the presence the
mentioned action-dependent state. In this work, two extensions of the original
action-dependent channel are studied. In the first, the decoder is interested
in estimating not only the message, but also the state sequence within an
average per-letter distortion. Under the constraint of common knowledge (i.e.,
the decoder's estimate of the state must be recoverable also at the encoder)
and assuming non-causal state knowledge at the encoder in the second phase, we
obtain a single-letter characterization of the achievable rate-distortion-cost
trade-off. In the second extension, we study an action-dependent degraded
broadcast channel. Under the assumption that the encoder knows the state
sequence causally in the second phase, the capacity-cost region is identified.
Various examples, including Gaussian channels and a model with a "probing"
encoder, are also provided to show the advantage of a proper joint design of
the two communication phases.
