On feedback, cribbing, and causal state-information on the multiple-access channel

We show that the capacity region of the state-dependent multiple-access channel (SD-MAC) with strictly-causally cribbing encoders is not enlarged if strictly-causal state-information (SI) and feedback are furnished to the encoders. We also derive the capacity region of the SD-MAC with causal SI at the cribbing encoders and show that Shannon strategies are optimal. Such strategies are generally suboptimal if the encoders access distinct SI. However, Shannon strategies are optimal and we have a characterization of the capacity region for the case where both encoders crib, causal SI is revealed to one encoder, and feedback is available to the other encoder.