# The Prisoners Dilemma Powerpoint Slides - Mason academic research

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Law and Economics:
The Prisoners’ Dilemma
F.H. Buckley Sciences Po October-November 2006 fbuckley@gmu.edu snelliga@gmu.edu

Goetz 1-16 Buckley 35-38
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Assignment for Thursday
 First Assignment: answer questions posed in the last paragraph of Goetz p. 19: assume that the choice is only between 0 doses and two doses

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The Prisoners’ Dilemma
 A simple game that has become the dominant paradigm for social scientists since it was invented about 1960.
 How the game works -- a simple narrative.
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PD games help to explain why we do dumb things
 Over-fish lakes and oceans
 Pollute  Arms race

 Fail to exploit bargaining gains
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Modeling PD games

 Game theoretic problems: payoffs for each player depend on actions of both

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Hollywood gets in the act

Russell Crowe as John Nash in “A Beautiful Mind”

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Modeling PD games

 Game theoretic problems: payoffs for each player depend on actions of both  Two possible strategies: A party cooperates when he performs valueincreasing promises, and defects when he breaches

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Modeling Two-party choice

Cooperate

Player 1

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Modeling Two-party choice

Player 1
Defect

10

Modeling Two-party choice: Player 2
Player 2
Cooperate

11

Modeling Two-party choice: Player 2
Player 2
Defect

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Modeling Two-party Choice: Both Cooperate
Player 2
Cooperate Cooperate
Both cooperate

Defect

Player 1
Defect

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Modeling Two-party Choice: Both Defect
Player 2
Cooperate Cooperate Defect

Player 1
Defect
Both defect

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Modeling Two-party Choice
Player 2
Cooperate Defect
Player 1 cooperates, Player 2 defects

Cooperate

Player 1
Defect

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Modeling Two-party Choice
Player 2
Cooperate Cooperate Defect

Player 1
Defect

Player 1 defects, Player 2 cooperates

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Modeling Two-party Choice
Player 2
Cooperate Defect
Player 1 cooperates, Player 2 defects

Cooperate

Both cooperate Player 1 defects, Player 2 cooperates

Player 1
Defect

Both defect

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Let’s examine Joint Cooperation
Player 2
Cooperate Cooperate
Both cooperate

Defect

Player 1
Defect

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Joint Cooperation: Omerta as a substitute for contracting
The food is better at the Tattaglias… I’m worried about Tessio…

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Joint Defection
Player 2
Cooperate Cooperate Defect

Player 1
Defect
Both defect

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Joint defection:

Can these gentlemen be acting efficiently?

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Player 1: Sucker’s Payoff
Player 2
Cooperate Defect
Player 1 cooperates, Player 2 defects

Cooperate

Player 1
Defect

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Sucker’s payoff:

Sucker performs, other party defects GONERIL Hear me, my lord; What need you five and twenty, ten, or five, To follow in a house where twice so many Have a command to tend you? REGAN What need one? KING LEAR O, reason not the need…
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Player 1: Defector’s Payoff
Player 2
Cooperate Cooperate Defect

Player 1
Defect

Player 1 defects, Player 2 cooperates

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Defector’s Payoff:

Defector breaches, sucker performs
"I can make them voting machines sing Home Sweet Home."

"Don't write anything you can phone. Don't phone anything you can talk. Don't talk anything you can whisper. Don't whisper anything you can smile. Don't smile anything you can nod. Don't nod anything you can wink."
Gov. Earl K. Long
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Let’s apply this to promising
Player 2
Cooperate Cooperate
Both cooperate: Omerta Player 1-defector’s payoff: Gov. Earl

Defect
Player 1 gets sucker’s payoff: Lear Both defect: The duelists

Player 1
Defect

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Modeling Promisor Choices
Player 2
Cooperate
Both Cooperate promise and perform Player 1 performs, player 2 breaches

Defect
Player 2 breaches, Player 1 performs Both defect: No one performs

Player 1

Defect

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Plugging in payoffs

First number is payoff for Player 1, Second number is payoff for Player 2

Player 2
Cooperate Cooperate 3, 3 Defect -1, 4

Player 1

Defect

4, -1

0, 0

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Defection dominates for Player 1

Cooperate Cooperate 3

Defect -1

Player 1
Defect


4


0

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Defection dominates for Player 2
Player 2
Cooperate Cooperate 3 Defect

Defect

-1




4

0

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Defection dominates: Goetz pp. 10-11

Cooperate Cooperate a

Defect c

Player 1
Defect


b


d

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I am always better off if the opponent cooperates: Goetz pp. 10-11

Cooperate Cooperate a

Defect c



Player 1
Defect b d



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a+a is greater than any other summation of payoffs
Player 2
Cooperate Cooperate a+a Defect c+c

Defect

b+b

d+d

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The paradox of the PD game
 While cooperation is collectively rational, defection is individually rational.

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The paradox of the PD game
 While cooperation is collectively rational, defection is individually rational.

 The undersupply of cooperation is “the tragedy of the commons.” Garrett Hardin, The Tragedy of the Commons (1968).

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The Tragedy of the Commons and the Law of the Sea

)
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An application from David Hume:

Your corn is ripe today, mine will be so tomorrow…

Treatise on Human Understanding III.ii.V (1739)
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University vs. Eager Goetz p. 7

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University v. Eager: Goetz p. 7
How would you plug in the payoffs?

Player 2
Cooperate Cooperate Defect

Player 1

Defect

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University v. Eager

Joint Defection: Everyone cheats and Exam does not signal any useful information

Player 2
Cooperate Cooperate Defect

Player 1

Defect

0,0

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University v. Eager

Joint Cooperation: No one cheats and exam measures true performance

Player 2
Cooperate Cooperate ?,? Defect

Player 1

Defect

Ex ante, are the positions symmetrical?
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University v. Eager

Sucker’s Payoff when one cooperates and the other defects

Player 2
Cooperate Cooperate Defect ?,?

Player 1

Defect

?,?

Will only the cheater get into med school?
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University vs. Eager Goetz p. 7

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Is the university at fault?
 An irresistible temptation?
 Is the penalty too high? How would you set it?

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The game of chicken

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Turning a PD game into a Chicken game.
What happens when joint defection is really bad?

Player 2
Cooperate Cooperate 3, 3 Defect -1, 4

Player 1

Defect

4, -1

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Turning a PD game into a Chicken game.
What happens when joint defection is really bad?

Player 2
Cooperate Cooperate 3, 3 Defect -1, 4

Player 1

Defect

4, -1

-∞, -∞

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Turning a PD game into a Chicken game.
Defection no longer dominates

Player 2
Cooperate Cooperate 3, 3 Defect -1, 4

Player 1

Defect

4, -1

-∞, -∞

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Turning a PD game into a Chicken game.
It might not be so drastic

Player 2
Cooperate Cooperate 3, 3 Defect -1, 4

Player 1

Defect

4, -1

-6, -6

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Can you think of applications?

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Can you think of applications?

The Chicken Game: the Canadian contribution to NATO ca. 1970

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Military spending during the Cold War as a Chicken Game
Player 2
Cooperate All parties make a fair military contribution Player 1 cheats, Player 2 a sucker Defect Player 1 a sucker, Player 2 cheats

Player 1

Cooperate

Defect

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Here’s another game: The Coordination Game
Player 2
1,1 0,0
Gives examples of this

Player 1
0,0 1,1

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Battle of the sexes as a variant of Coordination Games
Wife
Boxing Match Opera

Boxing Match

3,1

0,0

Husband
Opera 0,0 1,3

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PD Games and externalities Goetz p. 11
 How one acts affects other parties, for good or ill  These third party effects are called externalities

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Externalities may be good or bad

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Externalities may be good or bad
External goods

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Question 4, page 13:Urban renewal
What kind of a game is this?

Player 2
Cooperate Cooperate Defect

Player 1

Defect

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Question 4, page 13:Urban renewal
What kind of a game is this?

Player 2
Cooperate Cooperate Both beautify Defect

Player 1

Defect

Neither do

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Question 4, page 13:Urban renewal

One possible game: everyone beautifies their garden

Player 2
Cooperate Cooperate 3,3 Defect 2,1

Player 1

Defect

1,2

0,0

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Question 4, page 13:Urban renewal
Cleaning the commons as a chicken game

Player 2
Cooperate Cooperate 3,3 Defect -1,1

Player 1

Defect

1,-1

0,0

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Suppose your neighbors have organized a “clean-up day” for the commons
 Can you think of some excuses you might give your neighbors not to participate?  Would you expect other neighbors to come up with the same excuses?  What might militate against such excuses?
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Can social sanctions solve the incentive problem?
 Consider the following examples of cooperative behavior:
 Not littering  Showing up one time when one has agreed to meet a friend  Not betraying a friend  Helping out in an emergency: the Good Samaritan  Loyalty in wartime
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Can social sanctions solve the incentive problem?
 What changes when the game is repeated (or “iterated”)  Are there such things as high-trust and low-trust societies? Do some societies have a general tradition of keeping agreements?

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