I still remember when I read the data in business school 40 years ago, that Unions outside monopolies and oligopolies did not increase wages
I would argue that the American economy at large is essentially an oligopoly and that the automobile industry is definitely so
Just barely. The big three of today (GM, Ford, and Toyota) don't command even a majority of the US market between them. We have a big seven at the moment (GM, Ford, Toyota, Chrysler, Honda, Nissan, Hyundai/KIA) with the Germans a potential eighth if they could merge or even cooperate. Now while it is possible to have an oligopoly with that many players, the production overcapacity in the auto industry is still too great for any of the players to have oligopic pricing power which severely limits their ability pass cost increases to consumers.