Game Theory
Dr. Andrew L. H. Parkes
“Economics for Business (2)”
卜安吉
Nobel Memorial Prize in Economics

Eight gametheorists have
won the Nobel
Memorial Prize
in Economic
Sciences
April 5, 2012
Business Economics 2: Day 4
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John von Neuman
A brilliant
mathematician who’s
paper in 1928 was a
significant milestone in
creating the field of
game theory.
April 5, 2012
Business Economics 2: Day 4
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John von Neuman

was a Hungarian-American mathematician
and polymath who made major
contributions to a vast number of fields.

Von Neumann founded the field of game
theory as a mathematical discipline. Von
Neumann's proved his minimax theorem in
1928.
April 5, 2012
Business Economics 2: Day 4
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John Von Neuman

This theorem establishes
that in zero-sum games
with perfect information,
there exists a pair of
strategies for both players
that allows each to minimize
his maximum losses (hence
the name minimax).
April 5, 2012
Business Economics 2: Day 4
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Zero Sum Games

Zero-sum games
are those in which
one person's gains
exactly equal net
losses of the other
participant(s).
April 5, 2012
Business Economics 2: Day 4
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Perfect Information
 perfect
information means that players
know at each time all moves that have
taken place so far, for example
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Business Economics 2: Day 4
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A Nash Equilibrium

… is the solution to a
game involving two or
more players when
each player takes into
account the other
players’ known
strategies.
Jon Forbes Nash
A genius mathematician who created what has become known as the Nash Equilibrium.
April 5, 2012
Business Economics 2: Day 4
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A Nash Equilibrium

John Nash is the subject of the
Hollywood movie A Beautiful Mind.
Russell Crowe plays his part …
April 5, 2012
A Nash Equilibrium
results when no
player can improve
their situation as
long as others do
not change their
positions.
Business Economics 2: Day 4
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Prisoner’s Dilemma
 The
Prisoner’s Dilemma, is an
aspect of game theory that
examines why two individuals
might not agree, even if it
appears that it is best to do so.
April 5, 2012
Business Economics 2: Day 4
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Prisoner’s Dilemma
Cooperation is usually analyzed in game theory
Action of A\Action of B Cooperate
Defect
Cooperate
Fairly good [+ 5] Bad [ - 10]
Defect
Good [+ 10]
April 5, 2012
Business Economics 2: Day 4
Mediocre [0]
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Prisoner’s Dilemma
 There are two players
 And Two Choices
 To either “Cooperate" or to “Defect“
 The “Payoff Matrix” – is name for the
set of Choices
April 5, 2012
Business Economics 2: Day 4
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Prisoner’s Dilemma
 Each player gains when both cooperate
 But if only one of the players cooperates
 The defector gains more
 If both defect, both lose (or gain very little)
 However, both do not lose as much as the
"cheated" (the cooperator)
April 5, 2012
Business Economics 2: Day 4
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Prisoner’s Dilemma
The Origin of the Game
 A Crime was committed
 Two alleged criminals, both say I didn’t do it!
 Police (Cops) play “good cop, bad cop”
 Offer each a “DEAL” – I have a deal for YOU!
 Confess and you get a lesser sentence!
Therefore, this is the “Prisoner’s Dilemma.”
April 5, 2012
Business Economics 2: Day 4
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Prisoner’s Dilemma
If the Game is Zero Sum then:
 Both cooperate then result is 5
 One cooperates: receives +10
 One does not cooperate: receives – 10
 No one cooperated both receive 0!
 Therefore, zero sum game!
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Business Economics 2: Day 4
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