There are certainly examples of NE in repeated multiplayer games, such as a repeated prisoners dilemma. I believe multi-player poker's equilibrium to be similar if you were to exhaust it. You either get nothing in the long run, or less than nothing for deviating from dominant strategy.

It's safe to say chess is closer to being solved than poker.

In a tournament with a mixed field of players, even a GTO bot would get destroyed by a good exploitative player. So not even this is true.

Alrite, so, Game Theory Optimal has been solved. Thanks Rusty. I love when you back me up... But you did make a teeny little mistake there... Finding a perfect exploitative strategy to beat a specific set strategy is pretty much impossible in a real life situation, because, you will never know what that set strategy is. Unless you can read minds. Perhaps that's what you meant. "Finding a perfect exploitative strategy to a specific fixed strategy is actually very simple when you have telepathic powers"

At a theoretical level, but not really a practical level (some games are more solved than others)

Yes, you have to know what the fixed strategy is to find the counter strategy

It would depend on the terms of the tournament somewhat, but in most human-scale tournaments, a GTO bot would have much better than "fair" odds to win (i.e. it would win more than 1/N with N players) but winning would not be assured.

Back to the OP. An alternative is to analyze a sport, preferably one that the professor enjoys. That is, if you want to kiss ass. You'll enjoy the project, though not as much as poker, and the professor will enjoy it more than if it were about poker.

Baseball.

By definition a Nash Equilibrium is where neither player can deviate from his or her strategy to gain EV for their own strategy. With collusion you have players cooperating to change another player's strategy so it violates a Nash Equilibrium by definition.

It's certainly interesting and relevant to talk about cooperation and collusion in game theory, but I think what whosnext was trying to say is that it doesn't make sense to talk about those things in the context of Nash Equillibria.

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Yes, yes, I understand all that, but what I am saying in the context of a repeated game it makes perfect sense, which you'd follow if you listened to the lecture. Cartels are one of the examples used in the videos regarding collusion and NE.

You can also read the section of N-Player games in Further Limit Hold'em by Newhall. There is also the classic example of checking down to eliminate someone in a tournament.

TBH, whosnext didn't actually make any points whatsoever, and I have no idea what his education background is, either.

Tourneys and drug dealing are positive sum games.

The tourney itself is zero-sum, but the subgame with the hand to eliminate someone is not. Two can benefit to the expense of a third as described also by Newhall. I have studying to do though, so unless there's a point coming addressing what I've mentioned, and cited, I'm done.

The situation you're describing for tourneys happens when you're in the money or close to it; this is not zero sum in terms of tourney ev.

Hmmm, this has got me thinking...

I wonder how good/bad GTO is in a tournament.

Your 1/N is just a pure guess. It would depend on the tournament structure a lot, as you say. It would also depend on how exploitable the player pool was. And funnily enough, the worse the general pool of players, the less chance the GTO player stands of beating a good exploitative player.

Lets imagine a GTO bot were playing against loads of super fish and a few good exploitative players, or we could go even further, and say that were deep too, and that only 1 player takes the prize. In this not massively unlikely situation the GTO bot would blatantly get destroyed! It wouldn't be unbeatable at all. The exploitative players will build stacks much faster than the GTO player. They will gain strength via their coin which will enable them to beat GTO way more often than GTO beat them.

Hmmm... This also means that GTO players will all make more money as more and more people use GTO. If there were less GTO players in the tournament the GTO players would stand less of a chance.

... Those of you who have studied game theory often talk about co-operation in games. As an honest poker player I thought this never applied to me. But I guess I was wrong. Is there another word for what these guys are doing?? The exploitative player is working with the fish without the fishes knowledge so as to beat GTO. And none of the GTO players know what they are doing, but still, they are all working together to take that advantage away from the exploitative players.

Bloody GTO, just keeps getting worse and worse.

I watched the video and to me there is no mention of cooperation or collusion, but then again I have never seen cooperation or collusion rigorously defined in game theory.

Collusion seems to be implied in minmax strategies but that's not necessarily a part of a Nash Equilibrium.

I am not sure how cooperation would be defined in game theory. Something like an agreement between 2 players so that each improves their EV? I don't know if that even works or is relevant. Any way I would love to hear your thoughts on my random musings here.

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Collusion (or cooperation) is a set of players acting to maximise their combined pay-off. Secondly, in a Bayesian game, players may share their private information with some other players which can be termed cheating or collusion. Usually these definitions work well but I would always clearly state in what sense I intended to use the words at the beginning of an argument.

I'll try to flesh-out and outline what I'm trying to say as soon as I can (like Monday, bad timing, weekend planned, etc.). I am a mere student fwiw. I am glad to participate in the stimulating discussion we're having.

I think some of us get what you're talking about.

You think that the collusion and recollusion and exploiting and coexploiting and reexploiting repeat ad nauseum until no other collusion can occur? Ok, that's fine. I think it ends exactly the way it begins; with no acts of coexploitation nor collusion.

I have nothing but concept in my mind to back this up. So here's some salt:

****

Yes, collusion I mean what would commonly be called cooperation. Newall wrote about it in his book FLH with sections on N-player games. When the pot gets a size, and there are other players in the pot, then people try to "knock each other out", and in doing so are co-operating. But, it's not sharing information, or crossbooking, etc. I have nothing original to add. So, rather than re-write, I'd encourage people to read it.

Also, poker is solved as the joke goes. It's 0 EV not to play. You'll never have to post a BB again!

Bumping in case you forgot about this.

I've read the section in Further Limit Holdem referenced upthread, but I think what you're missing is the possibility of counter exploitation by a blind, which will dissolve any alliances before they ever come to fruition.

Also, Nash even titled his work as "non cooperative games" or something like that, so it seems that the idea that cooperation is a part of nash equilibrium is inherently flawed.

Collusion is a proven method for two players to profit versus a third player who is optimal. If the prisoners can communicate then there is no prisoners dilemma. This is not cheating, but the two players would play opposite solutions and crossbook the results.

FWIW this is why most criminals just lawyer up and don't fall for the hard sell from the interrogators in real life. The criminals have predetermined to take the "no fink" line.

Right, but the point is that Nash proved that there is a minimum ev in non cooperative games, not that there is a minimum ev in cooperative games, which there is not.

Since humour does not always do well hereabouts, I'll ruin my input before I make it, but what follows is both semi-ironic and semi-serious...

And ditto "theory".

In fact the only accurately appropriate word in the expression "GTO" is "game".

There have been critical essays written on an inordinate amount of applications, including animals and insects playing a game. If you are not already a member, you may want to consider joining

https://www.academia.edu/

You will probably not live long enough to digest all the papers submitted on game theory.

Unfortunately...

that is very accurate. If your advisor happens to be a poker buff, bon appetit!

So maybe nice to give an update on this year so far.
I really liked the track Game Theory and Behavioral Economics. The game theory subjects were my favorites but I don't think it really improved my poker game except the intellectual challenge. If you look at my Sharkscope graph (RubenHarm) you can clearly see a positive trend since September but I personally think this is mainly because I started playing more exploitative and less tried to play GTO.

One more thing, I now only have to finish my thesis to graduate. It would be nice if you could help me by doing this short experiment about individual decision-making.
It takes less then 10 minutes and you can win up to 100 euro with it.


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