That is just naive game theory. Humans can actually cooperate if cooperating makes everyone better off even if game theory says they shouldn't cooperate, has been tested and shown to be true over and over.
So the question is if the companies collectively benefits from colluding? If yes then they probably will do so, at least when the number of competitors are small and inhouse alternatives are expensive.
I don’t see what that mechanism or regulation would be for, say, pork prices. It seems far more likely that accurately collated pricing information is simply driving efficiency for each individual supplier.