Incorrect. Game theory predicts pollution. You just need to make sure the game has the correct predicted payoffs for each move, and the set of moves you want to measure, and their interactions...
You'll find Game Theory a lot easier to understand if you mentally replace every instance of "Math" with "AI". (So instead of saying "The Nash Equilibirum is...", just say "I trained an RNN and this is how it would play"). That's really all it is. Usually the games are designed in a simple way because the "AI" that is being run is nothing more complicated than min-cut/max-flow.
"Pollution" specifically is a case of the "Free-Rider Problem", and there are plenty of game theoretic results that explain it.