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JGWeissman comments on Decision Theory Paradox: PD with Three Implies Chaos? - Less Wrong
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If each TDT agent cares about its number of descendants, then they will instrumentally care about having a greater proportion of TDT agents to mutually cooperate with, and will therefore defect when one of the three players is a CDT agent, like the clique bot.
They only behave as you describe if they consider only the immediate, but not long term, consequences.
Seems correct to me. Judging agents with a different utility function than they use to decide will lead to them looking stupid.
I mentioned this to JGWeissman privately at the time, but I want to confirm now that this was exactly the solution I intended.