This account of decision theory/game theory seems like unnecessary formalism. The single play-through token problem prisoners dilemma has 4 outcomes to consider and between those 4 outcomes, no matter what your opponent does, your outcome is better if you betray so you betray.

The difference with the mirror token problem is that you set it up so that there are explicitly only two outcomes to consider. you betray and get 100 dollars or you cooperate and get 200 dollars. Obviously you choose the one that has the higher expected value os you get 200 dollars. The problem has explicitly been set up so that it is impossible for you to betray him and him to cooperate with you, or for him to betray you and you cooperate with him, so with those outcomes no longer existing, it's just a straightforward decision of do you want 100 dollars or 200 dollars.

The "CDT" analysis for the mirrored token problem seems to proceed as though the player is being forced to be unaware that the two non-symmetric outcomes are impossible, which is just dumb. like "CDT fails when you force it not to pretend that the problem is different from what it actually is"

here's what the CDT analysis of the mirror problem should actually be :

• Change Give?
  to be a constant function returning yes
• TheirDecision
  =give and so we get $200
• We get 200 dollars in expectation.
• Change Give?
  to be a constant function returning no
• TheirDecision
  =keep and so we get $100
• We get 100 dollars in expectation.

Obviously, 200 will be larger than 100 so CDT executes the dominant strategy which is give the token.