If both agents are FDT, and have common knowledge of each others source code
Any common knowledge they can draw up can go into a coordinating agent (adjudicator), all it needs is to be shared among the coalition, it doesn’t need to have any particular data. The problem is verifying that all members of the coalition will follow the policy chosen by the coordinating agent, and common knowledge of source code is useful for that. But it could just be the source code of the trivial rule of always following the policy given by the coordinating agent.
One possible policy chosen by the adjudicator should be falling back to unshared/private BATNA, aborting the bargain, and of course doing other things not in scope of this particular bargain. These things are not parts of the obey-the-adjudicator algorithm, but consequences of following it. So common knowledge of everything is not needed, only common knowledge of the adjudicator and its authority over the coalition. (This is also a possible way of looking at UDT, where a single agent in many possible states acting through many possible worlds coordinates among its variants.)
Any common knowledge they can draw up can go into a coordinating agent (adjudicator), all it needs is to be shared among the coalition, it doesn’t need to have any particular data. The problem is verifying that all members of the coalition will follow the policy chosen by the coordinating agent, and common knowledge of source code is useful for that. But it could just be the source code of the trivial rule of always following the policy given by the coordinating agent.
One possible policy chosen by the adjudicator should be falling back to unshared/private BATNA, aborting the bargain, and of course doing other things not in scope of this particular bargain. These things are not parts of the obey-the-adjudicator algorithm, but consequences of following it. So common knowledge of everything is not needed, only common knowledge of the adjudicator and its authority over the coalition. (This is also a possible way of looking at UDT, where a single agent in many possible states acting through many possible worlds coordinates among its variants.)