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…
There has been quite a bit of work (and several papers) on using CFR for games with >2 players. It is not theoretically guaranteed to converge to a Nash, and usually doesn't in practice either (there's one case in a toy…
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…
Hi - I'm one of the authors on this paper. We had professional designers do the figures for this paper; Fig3 in particular was far better than what we could do ourselves.
Hey, thanks for the mention! I've read hacker news for years, this seems like a good reason do de-lurk. If anyone has questions, I'm happy to answer them. I wrote that summary for a pretty broad target audience, and the…
Not quite: it really does only go to Nash in a 2p zero sum game. In a multiplayer zero-sum game, there's no theoretical proof that it should go to Nash. In the tiny 3p game of 3p Kuhn poker (3 players, 4 card deck,…
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…
There has been quite a bit of work (and several papers) on using CFR for games with >2 players. It is not theoretically guaranteed to converge to a Nash, and usually doesn't in practice either (there's one case in a toy…
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…
Hi - I'm one of the authors on this paper. We had professional designers do the figures for this paper; Fig3 in particular was far better than what we could do ourselves.
Hey, thanks for the mention! I've read hacker news for years, this seems like a good reason do de-lurk. If anyone has questions, I'm happy to answer them. I wrote that summary for a pretty broad target audience, and the…
Not quite: it really does only go to Nash in a 2p zero sum game. In a multiplayer zero-sum game, there's no theoretical proof that it should go to Nash. In the tiny 3p game of 3p Kuhn poker (3 players, 4 card deck,…