Even if there are a few game theoretic games in advanced papers that have limited information it would be a rather large stretch to say that economics incorporates limited information at this point in time. Maybe it's coming, I don't know ... It's not going to be soon.

A similar problem exists for 2. Yes I can find a paper or two, or probably even more that talk about it, but they don't exactly have a wide following because it just makes things too hard.

Incorporating both ? Can't even find a paper on it.