I think the Near Beer Game models your logically reduced version of the game, ignoring the original game’s irrelevant information and non-positive-value options for the intermediate players.
In this version, the manufacturer sees all the inventories, and all the middle layers pass all stock to the next layer. (The game also has a trivial demand function, so the only challenge is to detect or predict the single step change in demand rate, and then calculate 3 weeks ahead to smooth out the supply chain.)
https://forio.com/app/showcase/near-beer-game/
The game was played for 35 years before you demonstrated that it was a broken over-complication of a trivial game?
Or did you break the game by coordinating with your teammates on strategy (or, equivalently, all players computing the perfect Hofstadteran superrational strategy https://en.m.wikipedia.org/wiki/Superrationality
), when the game was meant to simulate the general human tendency for hyperlocal optimization, and the problem of dealing with chaotic incompetent peers?