Suppose we decide that proving systems are too (NP) hard and we want to restrict agents to polynomial time. If an agent has access to a random coin, can it interactively prove that its opponent is cooperative?

I stumbled across an interesting class of agent while attempting to design a probabilistically proving bot for AlexMennen's contest. The agent below always cooperates with opponents who always cooperate back, (almost) always defects against opponents who always defect against them, and runs in probabilistic polynomial time if its opponent does as well.

def mimic_bot(opponent):
    if random() > ε:
        my_source = quine_my_source()
        return eval(opponent, my_source) # do as your opponent does to you
    else:
        # unlikely, but necessary to break out of recursive simulations in polynomial time
        return COOPERATE

This particular agent is a bit naïve, but more sophisticated versions (e.g ones that do not cooperate with CooperateBot) are possible. Does anyone have any insight on probabilistically proving opponents will cooperate?