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CSC 5350 Assignment 1
Due date: 12 October 2009
1.
Consider a 3player strategic game
,(
),( )
ii
G
N A
u
.
Each player has
three available actions:
1
a
,
2
a
and
3
a
. That is,
1
2
3
1
2
3
{ ,
,
}
A
A
A
a a a
.
Suppose in
G
, player 1 always receives a payoff of 10 if he plays
1
a
, or 0
otherwise, regardless of what strategies the other two players play; player 2
always receives a payoff of 5 if he plays
2
a
, or 0 otherwise, regardless of
what strategies the other two players play; player 3 always receives a payoff
of 2 if he plays
3
a
, or 0 otherwise, regardless of what strategies the other
two players play.
(a)
Give the payoff matrix of
G
.
(b)
What are the pure strategy Nash equilibria in
G
?
(c)
An outcome
of a strategic game is said to be
Pareto optimal
if
there is no
other outcome
existing in the same game, such that
at least one player
i
gets a higher payoff in
than in
, while
no player gets a lower payoff in
than in
.
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This note was uploaded on 04/23/2010 for the course CSC CSC5350 taught by Professor Leunghofung during the Winter '09 term at CUHK.
 Winter '09
 LeungHoFung
 Computer Science

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