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Law and Economics The Prisoners Dilemma

• F.H. Buckley
• Sciences Po
• October-November 2006
• fbuckley_at_gmu.edu
• snelliga_at_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

3
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.

4
PD games help to explain why we do dumb things

• Over-fish lakes and oceans
• Pollute
• Arms race
• Fail to exploit bargaining gains

5
Modeling PD games

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

6
Hollywood gets in the act
Russell Crowe as John Nash in A Beautiful Mind
7
The need for poetic license
8
Modeling PD games

• Game theoretic problems payoffs for each player
  depend on actions of both
• Two possible strategies A party cooperates when
  he performs value-increasing promises, and
  defects when he breaches

9
Modeling Two-party choice
Player 1
10
Modeling Two-party choice
Player 1
11
Modeling Two-party choice Player 2
Player 2
12
Modeling Two-party choice Player 2
Player 2
13
Modeling Two-party Choice Both Cooperate
Player 2
Player 1
14
Modeling Two-party ChoiceBoth Defect
Player 2
Player 1
15
Modeling Two-party Choice
Player 2
Player 1
16
Modeling Two-party Choice
Player 2
Player 1
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Modeling Two-party Choice
Player 2
Player 1
18
Lets examine Joint Cooperation
Player 2
Player 1
19
Joint Cooperation Omerta as a substitute for
contracting
Im worried about Tessio
The food is better at the Tattaglias
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Joint Defection
Player 2
Player 1
21
Joint defection Can these gentlemen be acting
efficiently?
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Player 1 Suckers Payoff
Player 2
Player 1
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Suckers 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 Defectors Payoff
Player 2
Player 1
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Defectors 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
26
Lets apply this to promising
Player 2
Player 1
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Modeling Promisor Choices
Player 2
Player 1
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Plugging in payoffsFirst number is payoff for
Player 1,Second number is payoff for Player 2
Player 2
Player 1
29
Defection dominates for Player 1
Player 1
?
?
30
Defection dominates for Player 2
Player 2
?
?
31
Defection dominates Goetz pp. 10-11
Player 1
?
?
32
I am always better off if the opponent
cooperates Goetz pp. 10-11
?
Player 1
?
33
aa is greater than any other summation of payoffs
Player 2
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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. EagerGoetz p. 7
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University v. Eager Goetz p. 7How would you
plug in the payoffs?
Player 2
Player 1
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University v. EagerJoint Defection Everyone
cheats and Exam does not signal any useful
information
Player 2
Player 1
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University v. EagerJoint Cooperation No one
cheats and exam measures true performance
Player 2
Player 1
Ex ante, are the positions symmetrical?
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University v. EagerSuckers Payoff when one
cooperates and the other defects
Player 2
Player 1
Will only the cheater get into med school?
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University vs. EagerGoetz 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
Player 1
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Turning a PD game into a Chicken game.What
happens when joint defection is really bad?
Player 2
Player 1
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Turning a PD game into a Chicken game.Defection
no longer dominates
Player 2
Player 1
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Turning a PD game into a Chicken game.It might
not be so drastic
Player 2
Player 1
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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
Player 1
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Heres another gameThe Coordination Game
Player 2
Gives examples of this
Player 1
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Battle of the sexes as a variant of Coordination
Games
Wife
Husband
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PD Games and externalitiesGoetz 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 badAn external bad
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Externalities may be good or badExternal goods

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Question 4, page 13Urban renewalWhat kind of a
game is this?
Player 2
Player 1
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Question 4, page 13Urban renewalWhat kind of a
game is this?
Player 2
Player 1
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Question 4, page 13Urban renewalOne possible
game everyone beautifies their garden
Player 2
Player 1
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Question 4, page 13Urban renewalCleaning the
commons as a chicken game
Player 2
Player 1
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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?