In this lecture, the professor says that all Nash Equilibria have the same utility in non-atomic selfish routing, whereas this is not guaranteed in atomic selfish routing. It is unclear how general the statement is intended to be.
Does this hold for games in general? If a game is played by a sufficiently large number of nearly-identical players, such that none of them has "market power" to meaningfully manipulate utility, does that guarantee that all Nash Equilibria have identical utility? Are asymmetries in utility at Nash Equilibria only a product of at least one player having "market impact" on utility? If so, how can one intuitively see that this fact actually holds?