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"so, participants use models and apply them to change behavior, making the system harder to model (!)"

I am ignorant here, but isn't this property true of iterated prisoner dilemma situations? Is game theory not an adequate model here?

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That property is true of game theory problems, of which iterated prisoners dilemmas are a subset. And yes, game theory is the appropriate field to deal with those issues, however that does not necessarily mean that any solutions exist or are trivial for a specific problem.

Compare to a lot of engineering models being reduced to "just calculus"

I mean there are a lot of questions that can be posed, but are computationally intractable to answer. Think of the traveling salesman problem. Or worse - the halting problem.

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