Extensive Form Games

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# Extensive Form Games - PowerPoint PPT Presentation

Extensive Form Games. 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  by Joseph E. Harrington, Jr.

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### Extensive 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

Describe the Matching Pennies game that we discussed on Tuesday in extensive form notation and also in strategic form notation.

Clicker Test(to check that you are registered)

Do you have a working i>clicker with you?

• Yes
• No, I just clicked my ballpoint pen.
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 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: 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 PenniesStrategic Form of Game

Player 2

Tails

Player 1

Tails

More complicated game

Player 1

C

D

Player 2

2

0

E

F

Player 1

3

1

G

H

0

0

1

2

4 Possible Strategies for Player 1 :

What are they?

2 Possible Strategies for Player 2:

What are they?

Strategic Form

Player 2

E

F

C,G

C,H

Player 1

D,G

D,H

Prisoners’ Dilemma Game

Player 2

Cooperate

Defect

P

LAyER 1

Cooperate

Defect

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?

Battle of the sexes

Alice and Bob love to be together, but they don’t agree about where.

Stereotypic version.

Alice loves opera.

Bob loves fights.

Each would rather be together at less preferred event than to be apart, but each would prefer favorite event.

Cournot Equilibrium

Two firms each choose quantity.

Price is lower the greater is total output.

Profits of a firm are price times its own quantity

minus costs.