I don't know of a survey paper on CFR for multiplayer, but it's been showing up in conference papers and theses.

Here's a link to a shorter conference paper where CFR does converge to a Nash, in 3p Kuhn poker. It describes a family of equilibria, where one player (the second to act, IIRC) has a parameter that can't affect their own EV (...or else it wouldn't be a Nash), but does determine how much the other two players win/lose from each other. This illustrates the problem in equilibria for multiplayer games: if you're players 1 or 3, then even if you are playing a Nash, and everyone else does too (albeit different equilibria), then you can still lose. https://webdocs.cs.ualberta.ca/~games/poker/publications/AAM...

For a longer read, the best I know of is probably Rich Gibson's PhD thesis. He focussed on CFR for multiplayer games.

https://webdocs.cs.ualberta.ca/~games/poker/publications/gib...

Thanks again. So I guess for multiplayer games a better approach would be reinforcement learning with no game theoretic heuristics?

Game theory is always applicable to games :-)

Nash equilibrium is just one aspect of some games.

Game theory is domain specific. Generic methods in AI tend to dominate domain knowledge over time. Although I agree that other game-theoretic techniques might help here.

Game theory is specific to the domain of agents optimizing outcome in adversarial, cooperative, or (rarely) solitary systems. That's a pretty big domain.