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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
I don't know if this is something
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
that you could just summarize.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There's perfect information games
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
where all the information's on the table.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There is imperfect information games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There's repeated games that you play over and over.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There's zero sum games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There's non zero sum games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And then there's a really important distinction
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you're making, two player versus more players.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So what are, what other games are there?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And what's the difference, for example,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
with this two player game versus more players?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
What are the key differences in your view?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So let me start from the basics.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So a repeated game is a game where the same exact game
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
is played over and over.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
In these extensive form games, where it's,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
think about three form, maybe with these information sets
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
to represent incomplete information,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you can have kind of repetitive interactions.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Even repeated games are a special case of that, by the way.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But the game doesn't have to be exactly the same.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
It's like in sourcing auctions.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Yes, we're gonna see the same supply base year to year,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but what I'm buying is a little different every time.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And the supply base is a little different every time
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and so on.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So it's not really repeated.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So to find a purely repeated game
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
is actually very rare in the world.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So they're really a very course model of what's going on.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Then if you move up from just repeated,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
simple repeated matrix games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
not all the way to extensive form games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but in between, they're stochastic games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
where, you know, there's these,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you think about it like these little matrix games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And when you take an action and your opponent takes an action,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
they determine not which next state I'm going to,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
next game I'm going to,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but the distribution over next games
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
where I might be going to.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So that's the stochastic game.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But it's like matrix games, repeated stochastic games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
extensive form games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
That is from less to more general.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And poker is an example of the last one.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So it's really in the most general setting.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Extensive form games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And that's kind of what the AI community has been working on
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and being benchmarked on
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
with this Heads Up No Limit Texas Holdem.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Can you describe extensive form games?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
What's the model here?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Yeah, so if you're familiar with the tree form,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
so it's really the tree form.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Like in chess, there's a search tree.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Versus a matrix.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Versus a matrix, yeah.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And the matrix is called the matrix form
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
or bi matrix form or normal form game.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And here you have the tree form.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So you can actually do certain types of reasoning there
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
that you lose the information when you go to normal form.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
There's a certain form of equivalence.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Like if you go from tree form and you say it,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
every possible contingency plan is a strategy.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Then I can actually go back to the normal form,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but I lose some information from the lack of sequentiality.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Then the multiplayer versus two player distinction
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
is an important one.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So two player games in zero sum
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
are conceptually easier and computationally easier.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
They're still huge like this one,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but they're conceptually easier and computationally easier
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
in that conceptually, you don't have to worry about
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
which equilibrium is the other guy going to play
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
when there are multiple,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
because any equilibrium strategy is a best response
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
to any other equilibrium strategy.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So I can play a different equilibrium from you
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and we'll still get the right values of the game.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
That falls apart even with two players
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
when you have general sum games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Even without cooperation just in general.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Even without cooperation.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So there's a big gap from two player zero sum
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
to two player general sum or even to three player zero sum.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
That's a big gap, at least in theory.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Can you maybe non mathematically provide the intuition
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
why it all falls apart with three or more players?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
It seems like you should still be able to have
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
a Nash equilibrium that's instructive, that holds.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Okay, so it is true that all finite games
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
have a Nash equilibrium.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So this is what John Nash actually proved.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So they do have a Nash equilibrium.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
That's not the problem.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
The problem is that there can be many.
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