Example:
Two persons accused of being partners in a crime are arrested and
placed in separate cells so they cannot communicate with each other.
Without
a confession from one of the suspects, the district attorney has insufficient
evidence to convict them of the crime.
Both prisoners have the option of
remaining silent or squealing on their partner.
To extract a confession, the
district attorney tells each suspect the following consequences of his and his
partner’s actions.
a) If one suspect confesses and his partner does not, the one who confesses can
go free and the other gets a stiff 10year sentence.
b) If both suspects confess, they each get a reduced sentence of 5 years.
c) If both suspects remain silent, they each go to jail for one year on a lesser
charge.
The payoff matrix is:
Don’t
confess
Confess
Don’t
confess
(1, 1)
(10, 0)
Confess
(0, 10)
(5, 5)
What is the best strategy for each prisoner?
Solution:
This is a famous problem in Game Theory, known as the Prisoner’s Dilemma.
First note that this is not a
zerosum game.
If one prisoner chooses to confess, his benefit (avoiding 10 years in prison) is not the other player’s
loss.
The ROW player has a dominant strategy, to confess. The same is true for the COLUMN player.
Thus, when
each prisoner strives to maximize his payoff independently, the pair is driven to the outcome (5, 5).
Note that this
outcome also corresponds to the maximin strategy for each player.
(We only have a minimax strategy for a column
player in a zerosum game.)
The outcome (1, 1), with better payoffs to both appears unobtainable when this game is
played without cooperation.
John Nash,
a
mathematician at Princeton University, shared the Nobel Prize in Economics
in 1994 for his work in Game Theory.
He is the subject of the movie
A
Beautiful Mind
, starring Russell Crowe as Nash, which won the 2001 Oscar
for Best Picture.
Is (5, 5) a Nash equilibrium?
Can the ROW player
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 Spring '08
 Storfer
 Game Theory, payoff matrix, following payoff matrix

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