Econ 171 Reminder Course requirements Class website Go to economics departmen t home page Under Links find Class pages then click on Econ 171 Textbook Games Strategies and Decision Making ID: 135049
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Slide1
Extensive and Strategic Form Games
Econ 171Slide2
Reminder: Course requirements
Class website
Go to economics departmen
t 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 Slide3
Rock, Paper, ScissorsSlide4
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?Slide5
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 turnSlide6
Clicker Question
How many strategies are possible for Player B
in the perfect information version of Rock-Paper-Scissors
3
6
9
12
27Slide7
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.Slide8
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
Slide9
Details of strategic form game
Set of PlayersFor 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.Slide10
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.Slide11
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.Slide12
Matching PenniesStrategic Form of Game
-1, 1
1,-1
1,-1
-1,1
Heads
Tails
Heads
Tails
Player 2
Player 1Slide13
Rock, Paper, Scissors—Simultaneous Move
0,0
1,-1
Rock
Paper
Scissors
Rock
Paper
ScissorsSlide14
More complicated game
Player 1
Player 1
Player 2
2
0
3
1
0
0
1
2
D
C
F
E
G
H
4 Possible Strategies for Player 1 :
What are they?
2 Possible Strategies for Player 2:
What are they?Slide15
Strategic Form
1, 2
3, 1
0, 0
3, 1
2, 0
2, 0
2, 0
2, 0
Player 2
E
F
Player 1
C,G
C,H
D,G
D,HSlide16
WMDs: What are the strategies?Slide17
Clicker Question 2
How many possible strategies are there for the U.S. in this game?
2
4
6
8
16Slide18
Prisoners’ Dilemma Game
10, 10
0,
11
11, 0
1, 1
Cooperate
Defect
Cooperate
Defect
P
LAyER
1
Player 2Slide19
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?
2
4
8
16
32Slide20
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?
2
3
4
16
32Slide21
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?Slide22
0 , 0
0 , 1
1, 0
-10, -10
Swerve
Swerve
Don’t Swerve
Don’t SwerveSlide23
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.”Slide24
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.
Slide25
So long…at least for now
.