What’s the gist? I’m very dubious anyone models at more than 1 level in 90% of cases outside of puzzles about perfect logicians with marks on their foreheads
apropos of that thread on Hans Witsenhausen (it’s a travesty that Aumann is practically a household name among the students of strategy and conflict, but not Witsenhausen)
Yeah, Witsenhausen notion of information state is the right lens on this. More levels of recursive analysis does not mean more primitive random information.
I have paper copies of a couple of his unpublished notes from a course in grad school... but this might give you a taste of what he's about. It's a fairly abstruse/t/technical field (decentralized stochastic control) https://users.ece.cmu.edu/~pgrover/files/EncyclopediaWitsenhausen.pdf…
Basically, he is known for exploring the question of "who knows what, when?" in distributed systems, and coming up with a clever counter-example showing some fundamental difficulties. The tldr of his contribution is "follow the primitive information" (like "follow the money")
His most insightful (and most abstruse) paper is on distributed situations where the game tree is not definable a priori, but evolves dynamically during play: given who knows what/when and what they can do with it, how can we know there are no deadlocks or race conditions.