[mikebjohanson]

Nash equilibria are still guaranteed to exist. But it's only the 2p zero-sum perfect recall case where an equilibrium has useful properties, like being robust against any opponent strategy, including a worst-case opponent who knows your strategy. In a multiplayer (> 2 players) game, opponents can collude against you and playing your part of a Nash gives no useful guarantees on performance. Even if they aren't colluding, in poker games, the presence of a bad player just before you in turn order can hurt your EV worse than their own. And even if all players independently compute their own Nash equilibria (there can be many) and use the piece for their position, then that combination of strategies may not itself be a Nash equilibria.

[xapata]

According to Wikipedia, and my memory from school, Nash equilibrium doesn't exist unless all players are aware of the optimal strategy and are seeking it.

[jumpCastle]

Thanks for the explanation. I will also appreciate a reference to a good survey paper if you are in the mood :)

[mikebjohanson]

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...

[jumpCastle]

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

[xapata]

Game theory is always applicable to games :-)

Nash equilibrium is just one aspect of some games.

[jumpCastle]

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.

[xapata]

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