This may be an evolving answer, because the question is, in some sense, a (useful) rabbit hole. I apologize if I don't go deeply into meta-games per se, as it's a little outside of my scope, which is non-chance games of perfect information, but I think it's worthwhile to think about the underlying problem of indeterminacy in relation to games in general.

Bounded Rationality* is a useful concept because it pre-supposes a condition of computational intractability. Computational intractability can be introduced into games in several forms:

- Complexity
- Hidden Information
- Randomness ("quantum" indeterminacy)

_{[For more details on my use of "quantum" in regards to randomness, see Deterministic Games.]}

The underlying purpose of game theory is to determine "optimal" strategies for any given problem. I put optimal in quotes because optimality is a spectrum, and subjective in a condition of computational intractability.

Thus, we cannot know if AlphaGo plays optimally, only that it played *more optimally* than Lee Sedol in 4 out of 5 games.

This is distinct from strongly solved games such as tic-tac-toe, where we can know with total certainty that a choice is optimal, because the problem of tic-tac-toe is computationally tractable.

Part of the confusion may be semantic, because the concepts are subtle and profound, and require language, what TS Eliot might have called "the intolerable wrestle with words and meanings." (For instance, I used hidden information above to avoid having to distinguish between incomplete and imperfect information.)

- Perfect Play is generally defined as a strategy that leads to the best possible outcome for a participant, regardless of the choices of the opponent.

Thus minimax is of central importance, and provided the foundation for game theory.

Even in games with incomplete information, whether "deterministic" (Battleship) or involving "quantum indeterminacy" (Prisoner's Dilemma), there are optimal strategies. For simultaneous games such as Dilemma and all of the numerous extensions minimax is used. In Battleship, there are at least three strategies of increasing optimality, and although there doesn't appear to be a strategy that can yield P > .5, if one player employs a more optimal strategy, they will win in aggregate. Even Rock, Paper, Scissors seems to have an optimal strategy, which blows my mind, and carries the caveat that I need to look into it more.

- Thus, perfect play, as defined, is certainly achievable, but does not necessarily connote (objectively) optimal choices, which is a little confusing, because "perfect" implies objectivity, a condition which is only possible in regard to tractable problems.

It is also important to note that there may not be a "winning" strategy in the sense of being better off than the opponent, and in this condition, perfect or optimal play is mitigation of loss.

*In terms of incomplete information games specifically, I think there's a case for extending the concept of Bounded Rationality is extended to include information that cannot be observed or "known".

Colloquially, this would include the "unknowns" (both known and unknown) and the "unknowable" (quantum indeterminacy and superpositions).

How deeply have you researched Game Theory? (I'm asking for context.) Even in games with incomplete information, whether "deterministic" (Battleship) or involving "quantum indeterminacy" (Prisoner's Dilemma), there are optimal strategies (for instance, binary search extended to a 2D model in Battleship, and minimax in simultaneous games.) Even Rock, Paper, Scissors seems to have an optimal strategy: https://arstechnica.com/science/2014/05/win-at-rock-paper-scissors-by-knowing-thy-opponent/

– DukeZhou – 2017-04-21T16:48:32.357Great question, btw! This is a central issue in my own research. – DukeZhou – 2017-04-21T16:50:29.380

I have little experience in game theory asides from reading a few things here and there. Regarding your examples, I was curious if there was any approaches to the problem in a more general sense – k.c. sayz 'k.c sayz' – 2017-04-21T16:52:39.177

Ok. I'm going to attempt a formal answer. Mega-props for bringing up Hofstadter, btw. – DukeZhou – 2017-04-21T16:53:51.967

Id read this paper out of the University of Alberta: http://science.sciencemag.org/content/early/2017/03/01/science.aam6960.full

– Jaden Travnik – 2017-04-21T17:10:48.467@JadenTravnik Thank you for the reference, but I am asking in regards to perfect play in a philosophical sense. In a sense the paper you mention is "better than human" but not "super-rational". – k.c. sayz 'k.c sayz' – 2017-04-21T17:15:53.177

Super-rationality is distinct from perfect play and connotes a meta-strategy that may be counter to optimal strategy from a minimax perspective. Right now, this is still in the realm of metaphysics, but that does not mean it will always be so

– DukeZhou – 2017-04-21T17:22:45.570(if we're lucky, that is, b/c it may have implications regarding the survival of our species in a physical, material sense, i.e. "cooperate or betray?" when dealing with AGI much smarter than ourselves, and also in regard to human vs. human "play" in the sense of competition i.e. partisan contexts)For context, I guess perhaps this paper would be example of "super-rational play" under perfect information? https://intelligence.org/files/ProgramEquilibrium.pdf

– k.c. sayz 'k.c sayz' – 2017-04-21T17:51:38.320@colourincorrect I've only had a chance to scan this paper, but it look

reallyinteresting. Thanks for linking. I'll let you know if I have anything useful to say about it. Also, I've made a small correction in my answer, and tried to explain why I take the route I do. PS respect for choosing such a mind-bendingly difficult problem to contemplate. Part of the reason I focus on non-chance, perfect information games is tonothave to deal with this subject. – DukeZhou – 2017-04-22T01:23:41.370Ok, I think I have the concise answer for you.

(Lots of convolutions to get there, including creating an analyzing the equilibrium in an iterative Dilemma;)I think the tension here is between objectively optimal outcome in terms of max benefit, and limiting downside in a condition of indeterminacy, which might be though of as subjectively optimal. – DukeZhou – 2017-04-23T18:59:38.643