Nash equilibrium :A Beautiful Mind - blonde girl example

(These comments apply to the film - I haven't read the book.) You'd think they'd have covered the concept of Nash Equilibriuma a little more accurately, since it's the concept that bears his name. In the film, the 'inspiration' for his discovering it occurs when Nash and three pals are drinking in a bar. Four women enter, led by a blonde who is clearly the pick of the bunch. Nash reasons that if they all go for the blonde, at most one of them will end up with her, and they won't then stand a chance with the other three. But if they divide the women amongst themselves first, they all have a chance of ending up with one.
There are two problems with this example; one technical, one presentational. The technical one is that (assuming the 'rules' are as described) there are of course multiple Nash equilbria here (even disregarding mixed strategies) where each is assigned a different girl. Each of them has a slightly different payoff for each player, depending on who is assigned the blonde. The problem is that the concept doesn't tell you WHICH Equilibrium will end up being played - so the whole blonde problem hasn't actually been solved. They could agree among themselves to co-ordinate in a certain way, but this isn't shown in the film, and is in fact a further game theory problem of its own, since they would each like to be the one with the blonde. It's disappointing a better example wasn't used.
The presentational problem is that film implies Nash Equilibrium is just a way of co-operating in a socially useful manner, when in fact it's almost the opposite (a set of individual best responses). There's no necessary reason why co-operation is the outcome in this situation. The blonde could have been so attractive it would have been worth a 25% shot at her rather than a certain go at one of the plainer girls, which would lead to a competitive outcome.
A much better example would be one where there was a DIFFERENCE between the individual and the social optimums. Let's say there was one girl being hit on by two men. Neither wants to be the one to leave the group and buy the drinks, because he'd lose his (50%) chance with her. It's individually best for them both to keep talking to her. But because neither has bought her a drink, she gets fed up and goes home. So what was the best decision for the individual was worse for the group. I'm sure there's any number of better examples which would have explained N.E. more effectively than the misleading one they use in the film.