Extensive and Strategic Form
Games
Econ 171
Reminder: Course requirements
• Class website Go to economics department
home page. Under Links, find Class pages,
then click on Econ 171
• Textbook: Games, Strategies, and Decision
Making by Joseph E. Harrington, Jr.
• Clicker: Available at campus bookstore
i>clicker Register your clicker at
www.i>clicker.com/registration
Rock, Paper, Scissors
Rock-Paper-Scissors
First let’s draw the game tree on the blackboard
for the game played with full information, where
Player A moves first.
How would we draw the game tree for this game
when players move simultaneously?
Vocabulary for Extensive form games
•
•
•
•
•
Decision Tree
Decision Node-Specifies whose turn
Branches-Options
Terminal Node—End of play
Payoffs—For each person at each terminal
node.
• Strategy—What will you do at each decision
node where it is your turn
Clicker Question
How many strategies are possible for Player B
in the perfect information version of RockPaper-Scissors
A) 3
B) 6
C) 9
D) 12
E) 27
What is a strategy?
• “A strategy is not a sequence of actions, but
rather a catalog of contingency plans, what to
do in every situation. ‘’ Harrington, page 34.
(Read this section with extra care.)
• A strategy is a list stating what you would do
at each possible decision node where it is your
turn.
Strategies for B in perfect information
rock, paper, scissors game
• A strategy for B in perfect rock, paper, scissors
answers 3 questions:
– what will I do if I see rock?,
– what will I do if I see paper?
– What will I do if I see scissors?
• There are 3 possible answers to each question. Hence
there are 3x3x3=27 possible strategies.
• Examples:
– Paper if rock, rock if paper, rock if scissors
– Or Rock if rock, scissors if paper, paper if scissors
And so on… 27 possibilities
Details of strategic form game
• Set of Players
• For each player a strategy set—list of all the
strategies that the player could choose.
Remember that a strategy tells everything you
would do on any occasion when its your turn.
• Strategy profile: List of strategies chosen by
every player.
• Payoff to each player depends on the strategy
profile that was chosen.
Two player game matrix
in strategic form
Make a two-by-two table with one row for each
strategy that player 1 could choose and one
column for every strategy that player 2 could
choose.
Enter payoffs to players 1 and 2 in appropriate
spots.
Example: Simultaneous Move
Matching Pennies
• In this case each player has only two possible
strategies. Choose Heads, Choose tails.
• Payoff to Player 1 (row chooser) is written
first, then payoff to Player 2.
Matching Pennies
Strategic Form of Game
Player 2
Heads
Player 1
Heads
Tails
Tails
-1, 1
1,-1
1,-1
-1,1
Rock, Paper, Scissors—
Simultaneous Move
Rock
Rock
Paper
Scissors
0,0
Paper
1,-1
Scissors
More complicated game
Player 1
C
D
Player 2
Player 1
G
1
2
E
F
3
1
H
2
0
0
0
4 Possible Strategies for Player 1 :
What are they?
2 Possible Strategies for Player 2:
What are they?
Strategic Form
Player 2
E
Player 1
F
C,G
1, 2
3, 1
C,H
0, 0
3, 1
2, 0
2, 0
2, 0
2, 0
D,G
D,H
WMDs: What are the strategies?
Clicker Question 2
• How many possible strategies are there for
the U.S. in this game?
A) 2
B) 4
C) 6
D) 8
E) 16
Prisoners’ Dilemma Game
Player 2
Cooperate
P
L
A Cooperate
y
E
R
1
Defect
Defect
10, 10
0, 11
11, 0
1, 1
Clicker Question 3
Players A and B play two rounds of simultaneous
move prisoners’ dilemma. They don’t get to see
how the other player played until both rounds are
over. How many strategies are possible for each
player?
A) 2
B) 4
C) 8
D) 16
E) 32
Clicker Question 4
Players A and B play two rounds of simultaneous
move prisoners’ dilemma. Each gets to see the
other’s move in round 1 before choosing an action
for round 2. How many strategies are possible for
each player?
A) 2
B) 3
C) 4
D) 16
E) 32
The game of Chicken
James Dean story.
Alternatively—Two animals both want a
resource. Each has two possible strategies.
Fight or give up. A fight is very bad for both of
them. How do we make an interesting game of
this?
Swerve
Swerve
Don’t Swerve
0, 0
Don’t Swerve
0 , 1
1, 0 -10, -10
Common Knowledge of a fact
• Three ladies in a railway car. All have dirty faces.
• They can see each other’s faces, but not their
own. Each would blush visibly if she knew her
own face was dirty.
• All are brilliant logicians and they all know this.
• The conductor comes into the car and announces
for all to hear.
“Someone in this car has a dirty face.”
Common Knowledge
Why should this news matter? All three can see two dirty
faces.
In fact, all three know that the others can see at least one
dirty face.
Lady 1 says, Suppose that my face is clean. Then Lady 2 will
see exactly one dirty face—that of Lady 3. Lady 2 will reason,
if my face is clean, then Lady 3 will see 2 clean faces. If Lady 3
saw 2 clean faces, she would know her face was dirty and
would blush.
If Lady 3 doesn’t blush, lady 2 would conclude that her own
face is dirty and would blush. Therefore if Ladies 2 and 3
don’t blush, Lady 1 must conclude that her own face if dirty.
So long…at least for now.