But the mechanisms by which we play those games will be evident in the brain, and the games themselves will be evident in our expectation-program memory. (I'm assuming here that sufficiently-advanced neuropsychology will be able to analyze the "software" running on each brain, not just the firmware, but even if that field ends up with a different name, that's what I'm talking about here.)

We may be able to model some sort of "objectively-good" cooperative-evolutionary game-players using mathematics, but those models would not necessarily represent us; there's nothing that says we're even evolutionarily stable as a species over the long term ;)