Critique
This is a very good start. Nice selection of topics and scope. In general I think the article would benefit from a more wiki-like style (see the wikipedia style guide for what is meant by that) and some more background for a few important concepts.
Some concrete points / suggestions:
"Bounded rationality is the idea that the rationality of individual is limited by resources and that, while logical axioms may not be transitive, those individuals are nonetheless acting rationally." -- is it necessary to talk about transitivity of logical axioms in the first sentence? Perhaps just full stop after resources?
"We"-form, not appropriate for a wiki. (I think..)
Does the article build on the concept of satisficing? Perhaps work into the text?
Related pages, spelling: "has application"
"Game Theory assumes unbounded rationality" -- not entirely true, game theory is flexible! Perhaps something like "In game theory, it is typically assumed that agents acts rationally". Then again, not quite sure..
Is the Ouroboros really relevant? I know you like snakes, but..
Title: "Compare to unbounded rationality" -- comparison?
"Classical economics à la von Neumann and Morgenstern" -- à la is not plain English? And Classical economics isn't really due to VN and M, more the modern game-theoretic foundations.
"complete, or asymptotically complete, rationality of agents, or at least the market as a whole." -- what does asymptotically complete mean? What is "the market as a whole"? Want some definitions here.
"Logical axioms in that world are transitive" -- Not completely clear what "that world" refers to. Also, logical axioms in themselves are not transitive, rather the '->'-relation in a logical system is transitive.
"Agents maximize the expected utility 'E'" -- This breaks standard notational conventions for the expectation operator. Perhaps best to leave out the symbol or to define utility properly.
Bounded Rationality should not be capitalized; it is not a proper name. See: https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Abbreviations
"It may be too much effort to imagine expected utility for all eternity given an action (which is what E is defined as)" -- what does it mean to 'imagine' expected utility? Also, you have not defined E.
Do you have any sources that show that "the alternative is a hard problem" It is not true that modeling bounded rationality is always a hard problem.
"... and other mind games are simplistic illustrations of this quality." -- are these examples really 'mind-games'? And are they 'simplistic illustrations of this quality'? Anyway, what is 'this quality', is it the quality of BR? Does this mean BR is a 'quality'?
"a competition between System 1 and System 2, the unconscious and conscious systems in the brain" -- Perhaps an idea to have a whole subsection about this and the preceding mind-games? Mention Tversky & Kahneman etc.
"Alternatively, or perhaps in complement" -- alternatively or in complement?
"This is because information acquisition is costly and at the far end of the spectrum, impossibly costly." I don't think costly needs to be in bold here. Also, what does it mean to be impossibly costly?
The discussion on sparsity refers to a set of terms that aren't really defined: "weighted model, pyramidal problems". It is not clear exactly what is meant by sparsity in this context, although the image helps. Perhaps just explain what sorts of 'models' you are talking about here..
Can you explain the "Sparse Bounded Rationality Algorithm"?
Reinforcement Learning -- also should not be capitalized. Is it scientific to say that BR and RL are 'cousins'?