How Useful is Adaptive Action?
Channels with action-dependent states, as defined in, are considered. While investigated the scenario of message dependent non-adaptive action sequences, this paper focuses on adaptive action sequences, where the action is a strictly causal function of the message and the state sequences. The capacity of such a channel is characterized for the case when the state information is available non-causally at the channel encoder and it is shown that the adaptive action is not useful in increasing the capacity. The capacity of the action-dependent additive Gaussian channel, which was left open is then characterized by showing the equivalence of the current setting to the problem of the cooperative Multiple Access Channel (MAC) with asymmetric state information at the encoders .