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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
there's a set of different states that we might be in,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but I don't know which one we're in.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Nash equilibrium tells me exactly
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
what is the probability distribution
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
over those real world states in my mind.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
How does Nash equilibrium give you that distribution?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So why?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
I'll do a simple example.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So you know the game Rock, Paper, Scissors?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So we can draw it as player one moves first
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and then player two moves.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But of course, it's important that player two
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
doesn't know what player one moved,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
otherwise player two would win every time.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So we can draw that as an information set
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
where player one makes one of three moves first,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and then there's an information set for player two.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So player two doesn't know which of those nodes
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
the world is in.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But once we know the strategy for player one,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Nash equilibrium will say that you play 1 3rd Rock,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
1 3rd Paper, 1 3rd Scissors.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
From that, I can derive my beliefs on the information set
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
that they're 1 3rd, 1 3rd, 1 3rd.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So Bayes gives you that.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Bayes gives you.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But is that specific to a particular player,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
or is it something you quickly update
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
with the specific player?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
No, the game theory isn't really player specific.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So that's also why we don't need any data.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
We don't need any history
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
how these particular humans played in the past
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
or how any AI or human had played before.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
It's all about rationality.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So the AI just thinks about
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
what would a rational opponent do?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And what would I do if I am rational?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And that's the idea of game theory.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So it's really a data free, opponent free approach.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So it comes from the design of the game
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
as opposed to the design of the player.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Exactly, there's no opponent modeling per se.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
I mean, we've done some work on combining opponent modeling
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
with game theory so you can exploit weak players even more,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but that's another strand.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And in Librarus, we didn't turn that on.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So I decided that these players are too good.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And when you start to exploit an opponent,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you typically open yourself up to exploitation.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And these guys have so few holes to exploit
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
and they're world's leading experts in counter exploitation.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So I decided that we're not gonna turn that stuff on.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Actually, I saw a few of your papers exploiting opponents.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
It sounded very interesting to explore.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Do you think there's room for exploitation
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
generally outside of Librarus?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Is there a subject or people differences
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
that could be exploited, maybe not just in poker,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but in general interactions and negotiations,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
all these other domains that you're considering?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Yeah, definitely.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
We've done some work on that.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And I really like the work at hybrid digested too.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So you figure out what would a rational opponent do.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And by the way, that's safe in these zero sum games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
two player zero sum games,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
because if the opponent does something irrational,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
yes, it might throw off my beliefs,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but the amount that the player can gain
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
by throwing off my belief is always less
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
than they lose by playing poorly.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So it's safe.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But still, if somebody's weak as a player,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you might wanna play differently to exploit them more.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So you can think about it this way,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
a game theoretic strategy is unbeatable,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
but it doesn't maximally beat the other opponent.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So the winnings per hand might be better
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
with a different strategy.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And the hybrid is that you start
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
from a game theoretic approach.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
And then as you gain data about the opponent
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
in certain parts of the game tree,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
then in those parts of the game tree,
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
you start to tweak your strategy more and more
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
towards exploitation while still staying fairly close
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
to the game theoretic strategy
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
so as to not open yourself up to exploitation too much.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
How do you do that?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Do you try to vary up strategies, make it unpredictable?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
It's like, what is it, tit for tat strategies
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
in Prisoner's Dilemma or?
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Well, that's a repeated game.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Repeated games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
Simple Prisoner's Dilemma, repeated games.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But even there, there's no proof that says
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
that that's the best thing.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
But experimentally, it actually does well.
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Tuomas Sandholm: Poker and Game Theory | Lex Fridman Podcast #12
So what kind of games are there, first of all?
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