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The capacity regions are determined for various communication situations in which one or both encoders for a multiple access channel crib from the other encoder and learn the channel input(s) (to be) emitted by this encoder. Most of the achievability proofs in this paper hinge upon the new concept of backward decoding. Also, the notion of Shannon strategies seems to be of crucial importance. It is demonstrated that in some situations parts of the total cooperation line are achievable. Moreover, it is proved that if the encoders and the decoder are allowed to be nondeterministic, the capacity regions are not increased.