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 Rock-Paper-ScissorsA) 3B) 6C) 9D) 12E) 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 PenniesStrategic Form of Game

-1, 1 1,-1

1,-1 -1,1

Heads Tails

Heads

Tails

Player 2

Player 1

Rock, Paper, Scissors—Simultaneous Move

0,0 1,-1Rock Paper Scissors

Rock

Paper

Scissors

More complicated gamePlayer 1

Player 1

Player 220

31

00

12

DC

FE

G H

4 Possible Strategies for Player 1 : What are they?

2 Possible Strategies for Player 2:What are they?

Strategic Form

1, 2 3, 1

0, 0 3, 1

2, 0 2, 0

2, 0 2, 0

Player 2E F

Player 1

C,G

C,H

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) 2B) 4C) 6D) 8E) 16

Prisoners’ Dilemma Game

10, 10 0, 11

11, 0 1, 1

Cooperate Defect

Cooperate

Defect

PLAyER 1

Player 2

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) 2B) 4C) 8D) 16E) 32

Clicker Question 4Players 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) 2B) 3C) 4D) 8E) 16

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?

0 , 0 0 , 1

1, 0 -10, -10

Swerve

Swerve

Don’t Swerve

Don’t Swerve

So long…at least for now.