4-7 Imperfect Information Extensive Form: Poker

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En provenance du cours de Stanford University

Game Theory

1781 notes

Stanford University

Game Theory

1781 notes

Popularized by movies such as "A Beautiful Mind," game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call `games' in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE. How could you begin to model keyword auctions, and peer to peer file-sharing networks, without accounting for the incentives of the people using them? The course will provide the basics: representing games and strategies, the extensive form (which computer scientists call game trees), Bayesian games (modeling things like auctions), repeated and stochastic games, and more. We'll include a variety of examples including classic games and a few applications. You can find a full syllabus and description of the course here: http://web.stanford.edu/~jacksonm/GTOC-Syllabus.html There is also an advanced follow-up course to this one, for people already familiar with game theory: https://www.coursera.org/learn/gametheory2/ You can find an introductory video here: http://web.stanford.edu/~jacksonm/Intro_Networks.mp4

À partir de la leçon

Week 4: Extensive-Form Games

Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies.

4-1 Perfect Information Extensive Form: Taste 3:59

4-2 Formalizing Perfect Information Extensive Form Games 6:15

4-3 Perfect Information Extensive Form: Strategies, BR, NE 13:40

4-4 Subgame Perfection 9:37

4-5 Backward Induction 13:01

4-6 Subgame Perfect Application: Ultimatum Bargaining17:50

4-7 Imperfect Information Extensive Form: Poker 3:36

4-8 Imperfect Information Extensive Form: Definition, Strategies 10:54

4-9 Mixed and Behavioral Strategies 8:53

4-10 Incomplete Information in the Extensive Form: Beyond Subgame Perfection 13:16

Rencontrer les enseignants

Matthew O. Jackson
Professor
Economics
Kevin Leyton-Brown
Professor
Computer Science
Yoav Shoham
Professor
Computer Science

Hello again, folks. so this is Matt and we're talking about Imperfect Information

in the Extensive Form now. So we're going to be talking now about

games where we have some sequential moves and there can be some uncertainty in

player's minds about both the possible pay-offs of other and the strategies that

others might be following. So we'll start let's just by, you know,

to, to give you some ideas about this, let's talk a little bit about poker.

which, as a game, has been becoming incredibly popular recently both for

people playing it on television and other kinds of things.

And it's one of the oldest games which has very extensive experience, and for,

for a lot of people. And the, the, the, you know, one of the

critical aspects of poker is that there's actually sequential play in betting,

calling, folding. So, one player gets, you know, to to make

a, a decision in terms of how much they're going to make a bet at a certain

point in time. Other players have to react to that.

So, the sequential play you see some cards in, in many of these

games, but not all. So you might see some of the cards that

the other players are holding. But you don't know how strong their hand

is. And you have to be inferring things about

their, their possible cards both from odds in the game and based on what

they're doing in terms of their strategy. so you see the bets and you react to them

and you have to make inferences based on that.

so that involves having beliefs about the motivations, the rationality of other

players what their pay-offs are, what their potential pay-offs are, which in

poker might come from, from the cards. so when we think about these kinds of

games, you know, there's many possible hands that's going to make poker a fairly

complicated game to, to keep track of. There's many batting strategies which

means that the overall tree that we, we're going to have to work with is, is

going to be quite complicated. so it's actually going to be almost

impossible to draw the tree in the sense of, of just drawing it out on the screen.

but there's nonetheless a lot that we can learn about analyzing such games.

And analyzing the types of strategies that they have.

How, how do we represent extensive form games with incomplete information? How

might we reason about these things? and moreover there'll be simpler settings.

you know, poker's actually a fairly complicated game.

and there, there's other fairly complicated games but very high stakes

games. So, for instance, you know, we could have

one country thinking about invading another one and, and, a potential war or

a conflict. they're trying to decide what the other

country's going to do in response. So, if you invaded, what would they do?

That's a game of incomplete information because you might not know exactly how

strong they are or how what's the, the willingness of the population to fight.

What might happen politically. how, how strong are they, if there was a war. so

there's, these are situations where one party might have to move first,

anticipating reaction of the other. the second one has to anticipate what

the, the, the fact that they're being invaded means about the strength of the

other do you surrender? Do you fight? so those are games that are going to have

similar kinds of features to these. And it's going to be very important to

develop a set of, a way of representing this things,

and some thoughts about analyzing those. So that's where we're headed next and

we'll see a lot more of this very shortly.

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