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EF4484Game TheoryLecture 6
10/22/2008
1
Dynamic Games of
Complete Information
ExtensiveForm Representation
Game Tree
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EF4484Game TheoryLecture 6
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Outline of dynamic games of complete
information
Dynamic games of complete information
Extensiveform representation
Dynamic games of complete and perfect
information
Game tree
Subgameperfect Nash equilibrium
Backward induction
Applications
Dynamic games of complete and imperfect
information
More applications
Repeated games
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EF4484Game TheoryLecture 6
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Today’s Agenda
Examples
Entry game
Sequentialmove matching pennies
Extensiveform representation
Dynamic games of complete and perfect
information
Game tree
Midterm Exam
4
Representations
The two representations of the rules of a game are
The normal (strategic) form
The extensive form
10/22/2008
EF4484Game TheoryLecture 6
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10/22/2008
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5
The Normal (Strategic) Form
The normal form of a game is represented as a matrix or
a table:
Rows correspond to the strategies
of
player 1
and columns
correspond to the strategies
of
player 2
.
In each
cell of the table
, we write the payoffs associated
with that pair of strategies.
Player 2
c
d
Player 1
a
3
,
4
5
,
2
b
1
,
1
0
,
6
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EF4484Game TheoryLecture 6
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The Extensive Form
The extensive form is represented as a game tree
.
A game tree starts from a root
: one of the players has
to make a choice.
The variable choices available to this player are
represented as branches
emanating from the root.
At the end of each one of the branches that emerge
from the root, it may split into further branches.
The payoffs are written at the end of the tree where
the game terminates.
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EF4484Game TheoryLecture 6
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Example: Entry game
An incumbent monopolist
faces the possibility of entry by
a
challenger
.
The
challenger
may choose to
enter
or
stay out
.
If the
challenger
enters, the
incumbent
can choose either to
accommodate
or
to
fight
.
The payoffs are common knowledge.
Challenger
In
Out
Incumbent
A
F
1
,
2
2
,
1
0
,
0
The
first number
is the
payoff of the challenger.
The
second number
is the
payoff of the incumbent.
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Example: Sequential matching pennies
Each of the two players has a
penny.
Player 1 first chooses whether
to show the Head or the Tail.
After observing player 1’s
choice, player 2 chooses to
show Head or Tail
Both players know the following
rules:
If two pennies match (both
heads or both tails) then
player 2 wins player 1’s
penny.
Otherwise, player 1 wins
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This note was uploaded on 02/22/2009 for the course ECONOMICS 4313 taught by Professor Tsui during the Spring '09 term at HKU.
 Spring '09
 tsui
 Game Theory

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