You actually wrote that there is no agreement in your first pragraph and that there is agreement in your last paragraph.
I understand that you mean that the first agreement is a written contract and that the second one is informal. Maybe, but that is not the point.
The point is that the franchisees of different chains agreed not to compete (at the golf club or elsewhere). Ergo: they are not really competitors.
In a capitalistic view, the Blue Burger franchise and the Yellow Burger franchise of Little Rock town would compete and that would also imply triying to offer the best service, which in turn implies trying to get the best personnel. That would not drive wages higher than what still allows them to make a profit, but that would make them readily accept the best employees of the other chain if they wished to jump ship and maybe also try to lure them in with better conditions. But, as you noted, they do not do that.
And in my admitedly limited experience in rural USA, fast food joints indeed do not compete. They basically all serve the same low quality food, have the same relatively low service level and similar prices. Interestingly, family owned restaurants usually had markedly better service when I was there, so maybe they are the only ones who are not part of the general non-competition agreement.
