1
ECON191 (Spring 2010)
15, 16 & 19.4.2010 (Tutorial 7)
Chapter 9 Introduction to Game Theory
(Chapter 13 of textbook)
What is game theory?
Game theory is a method for modeling decision making when decisions interact.
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).
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
IBM has 2 strategies:
D
and
U
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
Games of
sequential move
: prior moves are
observable.
Toshiba observed IBM’
s move when
Toshiba takes the move.
Toshiba knows which decision node she is
on when she has the move.
IBM has 2 strategies:
D
and
U
Toshiba has 2 strategies:
D
and
U
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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
Dominate strategy and dominated strategy
Dominate strategy: when one strategy is best for a player no matter what strategy the
other player uses.
We will explain these concepts with the classi
c 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.
We will represent the prisoner’s dilemma with normal form.
Bob
Confess
Deny
Ann
Confess
10, 10
2, 12
Deny
12, 2
3, 3
Is there any
dominated strategy
for Ann and Bob?
Let’s c
onsider Ann,
If Ann expects Bob to
confess
, then Ann should
confess
. (
–
10
–
12)
If Ann expects Bob to
deny
, then Ann should
confess
. (
–
2
–
3)
Ann gets a higher payoff with
confess
than
deny
no matter what she expects Bob to do.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 CHAN
 Game Theory, player, Dominant strategy, Ann

Click to edit the document details