Recap
Perfect-Information Extensive-Form Games
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11
February 13, 2007
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 1
Recap
Perfect-Information Extensive-Form Games
Lecture Overview
Recap
Perfect-Information Extensive-Form Games
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 2
Recap
Perfect-Information Extensive-Form Games
Introduction
I
The normal form game representation does not incorporate
any notion of sequence, or time, of the actions of the players
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 3
Recap
Perfect-Information Extensive-Form Games
Introduction
I
The normal form game representation does not incorporate
any notion of sequence, or time, of the actions of the players
I
The extensive form is an alternative representation that makes
the temporal structure explicit.
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 3
Recap
Perfect-Information Extensive-Form Games
Introduction
I
The normal form game representation does not incorporate
any notion of sequence, or time, of the actions of the players
I
The extensive form is an alternative representation that makes
the temporal structure explicit.
Two variants:
I
I
I
perfect information extensive-form games
imperfect-information extensive-form games
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 3
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
I
Each terminal node represents a possible final outcome of the
game
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
I
Each terminal node represents a possible final outcome of the
game
I
Usually written with the basal root on top
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
I
Each terminal node represents a possible final outcome of the
game
I
Usually written with the basal root on top
Parts of the tree are labeled as follows:
I
I
Internal nodes (including the root) are labeled with player
identifiers
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
I
Each terminal node represents a possible final outcome of the
game
I
Usually written with the basal root on top
Parts of the tree are labeled as follows:
I
I
I
Internal nodes (including the root) are labeled with player
identifiers
Branches are labeled with player choices
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Perfect-Information Extensive Form Representation
I
Represents a finite sequential game as a rooted tree
I
Each internal node represents a particular player’s ’turn’
I
Each branch from this internal node represents a different
choice for that player
I
Each terminal node represents a possible final outcome of the
game
I
Usually written with the basal root on top
Parts of the tree are labeled as follows:
I
I
I
I
Internal nodes (including the root) are labeled with player
identifiers
Branches are labeled with player choices
Terminal nodes are labeled with utility outcomes
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 4
Recap
Perfect-Information Extensive-Form Games
Example: the sharing game
q1
HH
2–0
2
q A
no AA yes
A
q
Aq
(0,0)
(2,0)
Extensive Form Games and Backward Induction
1–1
HH
H
q2
A
no AA yes
A
q
Aq
(0,0)
(1,1)
0–2
HH
H
HHq 2
A
no AA yes
A
Aq
q
(0,0)
(0,2)
ISCI 330 Lecture 11, Slide 5
Recap
Perfect-Information Extensive-Form Games
Example: the sharing game
q1
HH
2–0
2
q A
no AA yes
A
q
Aq
(0,0)
(2,0)
1–1
HH
H
q2
A
no AA yes
A
q
Aq
(0,0)
(1,1)
0–2
HH
H
HHq 2
A
no AA yes
A
Aq
q
(0,0)
(0,2)
Get with a partner and decide on a simple sequential game (e.g.
tic-tac-toe) and represent it in extended form
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 5
Recap
Perfect-Information Extensive-Form Games
Lecture Overview
Recap
Perfect-Information Extensive-Form Games
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 6
Recap
Perfect-Information Extensive-Form Games
Example: the sharing game
q1
HH
2–0
2
q A
no AA yes
A
q
Aq
(0,0)
(2,0)
Extensive Form Games and Backward Induction
1–1
HH
H
q2
A
no AA yes
A
q
Aq
(0,0)
(1,1)
0–2
HH
H
HHq 2
A
no AA yes
A
Aq
q
(0,0)
(0,2)
ISCI 330 Lecture 11, Slide 7
Recap
Perfect-Information Extensive-Form Games
Example: the sharing game
q1
HH
2–0
2
q A
no AA yes
A
q
Aq
(0,0)
(2,0)
1–1
HH
H
q2
A
no AA yes
A
q
Aq
(0,0)
(1,1)
0–2
HH
H
HHq 2
A
no AA yes
A
Aq
q
(0,0)
(0,2)
Play as a fun game, dividing 100 dollar coins. (Play each partner
only once.)
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 7
Recap
Perfect-Information Extensive-Form Games
Pure Strategies
I
In the sharing game (splitting 2 coins) how many pure
strategies does each player have?
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 8
Recap
Perfect-Information Extensive-Form Games
Pure Strategies
I
In the sharing game (splitting 2 coins) how many pure
strategies does each player have?
I
player 1: 3; player 2: 8
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 8
Recap
Perfect-Information Extensive-Form Games
Pure Strategies
I
In the sharing game (splitting 2 coins) how many pure
strategies does each player have?
I
I
player 1: 3; player 2: 8
Overall, a pure strategy for a player in a perfect-information
game is a complete specification of which deterministic action
to take at every node belonging to that player.
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 8
Recap
Perfect-Information Extensive-Form Games
Pure Strategies
I
In the sharing game (splitting 2 coins) how many pure
strategies does each player have?
I
player 1: 3; player 2: 8
I
Overall, a pure strategy for a player in a perfect-information
game is a complete specification of which deterministic action
to take at every node belonging to that player.
I
Can think of a strategy as a complete set of instructions for a
proxy who will play for the player in their abscence
Extensive Form Games and Backward Induction
ISCI 330 Lecture 11, Slide 8