There's a class of mimicking players that I'd like to discuss. Pseudocode of an example:

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 infinitely recursive simulations
        return COOPERATE

MimicBot's strategy will almost perfectly mirror its opponent's. Is there literature on a MimicBot, MirrorBot, PsychicTitForTatBot or something like that?

Aside: The source for MimicBot does not contain the DEFECT symbol, which might make it easier† for other programs to prove that MimicBot won't defect against them.

† easier but not trivial