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ECON191 (Spring 2009)
2021.4.2009 (Tutorial 9)
Chapter 9 Introduction to Game Theory
(Chapter 13 of textbook)
What is game theory?
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Game theory is a method for modeling decision making when decisions interact.
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A game is characterized by
(i)
The set of players
(ii)
The strategy set (the set of feasible actions)

A strategy is a
complete plan of action
, which tells the player what to do every time
where he has the move.
(iii)
The payoffs of the players

Payoff of a player depends not only on his own strategy, but also the strategy of the
other player (interdependence).
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In game theory, we assume players are rational and they are only interested in their own
payoffs.
Representation of games
(1)
Extensive form
(Game tree/Kuhn tree)

Decision nodes
: represents points in the game where a player takes an action.

Braches
at each decision node: represents the alternative actions that the player with
move can take.

Terminal nodes
: represents the final outcome of the game. Associated with each
terminal node is a payoff for every player.
(2)
Strategic from

Payoff matrices
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Games of
sequential move
: prior moves are
observable.
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Toshiba observed IBM’s move when
Toshiba takes the move.
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Toshiba knows which decision node she is
on when she has the move.
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IBM has 2 strategies:
D
and
U
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Toshiba has 2 strategies:
D
and
U
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First mover advantage
UNIX
DOS
UNIX
DOS
UNIX
DOS
600
200
100
100
100
100
200
600
IBM
TOSHIBA
TOSHIBA
IBM’s payoff
Toshiba’s payoff
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IBM has 2 strategies:
D
and
U
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Toshiba has 2 strategies:
D and U
Toshiba
DOS
UNIX
IBM
DOS
600, 200
100, 100
UNIX
100, 100
200, 600
IBM’s payoff
Toshiba’s payoff
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Dominate strategy and dominated strategy
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Dominate strategy: when one strategy is best for a player no matter what strategy the
other player uses.
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We will explain these concepts with the classic example of Prisoner’s Dilemma.
Example
:
Prisoner’s Dilemma
The story:
Ann and Bob have been caught stealing a car. The police suspect that they have also robbed
the bank, a more serious crime. The police has no evidence for the robbery, and needs at least
one person to confess to get a conviction.
Ann and Bob are separated and each told:
(i)
If each confesses, then each will get a 10 year sentence.
(ii)
If one confesses, but the other denies, then he will get 2 year and his accomplice will
get 12 yrs.
(iii)
If neither confesses, then each will get a 3 year sentence for auto theft.
orightshadlft
We will represent the prisoner’s dilemma with normal form.
Bob
Confess
Deny
Ann
Confess
10, 10
2, 12
Deny
12, 2
3, 3
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Is there any
dominated strategy
for Ann and Bob?
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Let’s consider Ann,
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If Ann expects Bob to
confess
, then Ann should
confess
. (–10
>
–12)
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If Ann expects Bob to
deny
, then Ann should
confess
. (–2
>
–3)
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Ann gets a higher payoff with
confess
than
deny
no matter what she expects Bob to do.
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 Spring '08
 Chen
 Microeconomics, Game Theory, player, Bob Ann

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