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gjm comments on Agent-Simulates-Predictor Variant of the Prisoner's Dilemma - Less Wrong Discussion
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Why not? Supposing roystngr to be correct, it's useful information for any reader that if they want to find game-theoretic discussions of related ideas they might want to look for "Chicken" rather than for "Prisoner's Dilemma". Supposing him to be incorrect, other readers might be as well able to correct him as Gram_Stone. Supposing him to be correct, other readers may be able to confirm that, which might be helpful to Gram_Stone.
I think roystngr is correct that the 2x2 matrix here is quite different from that for the PD, and somewhat resembles that of Chicken. It's not quite Chicken because a cooperating player is indifferent between cooperation and defection by the other player, whereas in Chicken a swerving player prefers the other player also to swerve (less loss of face).
Chicken famously has a counterintuitive property similar to the one described here: if you play Chicken with God, then God loses. (You commit to not swerving; God sees this and knows you will not swerve, and therefore must swerve.) I've always thought the obvious conclusion is that if there is a God then he doesn't play Chicken (and if you try to get him to, he refuses or changes the game or the payoff) -- but of course, as pointed out here, the same issue arises with someone who's merely very good at making predictions and doesn't have the other superpowers traditionally ascribed to God, and might therefore actually have nothing better to do than play.
It's not, as you observe, actually chicken, although it's more closely related to chicken than to the prisoner's dilemma. What it is even more similar to, with the addition of the perfect predictive agent, is the Ultimatum Game, which by the "counterintuitive" property you describe later, God would -also- always lose. (Which I don't know about, one of the properties God is usually described to have is a willingness to punish defectors.)
Which isn't to contribute to the terminology debate, but to point out that the discussion isn't actually furthered by endless debates over how to classify edge cases.
If God values punishing defectors enough, then that changes the effective payoffs in the game.
If God's predictive abilities matter, then I take it you're envisaging God in the role of proposer rather than responder, and the sense in which he loses is that e.g. the responder can commit to declining any offer less than (say) $9 from an initial stake of $10, so that God only gets $1. Well. The responder can do that against anyone, perfect predictor or not, and God actually does better than anyone else because he can at least offer the $9 he needs to. But I suppose the point is that the responder wouldn't make that commitment if not playing against God, because without God's magical foreknowledge the predictor won't be offering $9 anyway.
So, anyway, if I understand your parenthesis right, you're saying that it won't play out that way because for the responder to decline a reasonable offer is a variety of defection, and God will want to punish it by refusing to make the offer the responder wants. Perhaps so, but what that means is that God's true payoff isn't (say) $1 but $1 plus the fact of the responder's successful defection, and if he disvalues the second component of that enough it could be worse than $0. Which is true, but it means that they're no longer playing the Ultimatum Game, they're playing another game with different payoffs, and of course that can lead to different choices.