We consider a two-user multiple-access channel, where one of the encoders is allowed to take an action that affects the formation of the channel states. Two independent messages are sent: a common message known to both encoders and a private message known only to the informed encoder. In addition, the states are know non-causally to the informed encoder. We find precise characterizations of the capacity region. Our framework takes account of previously evaluated settings regarding point-to-point channels with actions and multiple-access channels with common messages. We focus specifically on the Gaussian channel, obtain the capacity region and compute it. In the process, we find the capacity of the Gaussian point-to-point action dependent channel, which was left open.
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