The compound MAC with common message and partial channel state information

We characterize the capacity region of the compound Discrete Memoryless Multiple Access Channel, where both transmitters have an additional common message. The channel state information is as follows: for each transmitter, there is a finite partition of the set of channels. Each transmitter knows which element of his partition the channel actually used belongs to. The capacity region is not affected by the amount of channel state information at the receiver, which may be arbitrary.