I think that the movie scene has sth to do with the Nash equilibrium.
Remember the Nash bargaining solution defines axioms (four, namely Pareto-efficiency, utility independence of affine transformations, independence of irrelevant alternatives, and symmetry) which a point (set) in the set of feasible allocations should fulfill.
Concerning the Nash equilibrium of the "bar-approaching blond girl game", it's very difficult to give the Nash equilibria. I think the information structure, the utilities and so on can be constructed such that almost any possible strategy combination could be a (bayesian) Nash equilibrium.