I think I have a proof that the only Nash equilibrium strategies for Dark playing against a perfect reasoner are those that lead to a uniform distribution over observed decks. K-complexity doesn’t seem to come into it. What Dark should do against an imperfect reasoner is a different question, which we can’t solve because we don’t have a good theory of imperfect reasoning.
I think I have a proof that the only Nash equilibrium strategies for Dark playing against a perfect reasoner are those that lead to a uniform distribution over observed decks. K-complexity doesn’t seem to come into it. What Dark should do against an imperfect reasoner is a different question, which we can’t solve because we don’t have a good theory of imperfect reasoning.