SID:_________________________
2
1.
Consider the following three-player game:
L
C
R
L
C
R
T
1,2,2
0,3,2
1,2,9
T
0,3,0
,3,1 1,2,2
B
2,1,7
±
,1,0 2,2,1
B
2,1,2
3,1,4
2,2,3
X
Y
For which values of
±
and
is the strategy
²
weakly dominated but not strictly dominated?
a)
± ³ ´
and
³ µ
.
b)
± ³ ³ ¶·
.
c)
± ³ ³ ´
.
d)
± ³ ³ ·
.
2.
A normal form game is defined by:
a)
A payoff matrix.
b)
A set of players, a strategy profile for each player, and a Bernoullian utility function
for each player defined over the set of strategy profiles.
c)
A set of players, a strategy profile for each player, a Bernoullian utility function for
each player defined over the set of strategy profiles and a Nash equilibrium.
d)
Two players and a matrix.
3.
Let
¸ ³ ¹±º º »¼
and suppose that an agent’s preferences are characterized by a Bernoullian
utility function
½¾ ¸ ¿ À
that satisfies
½Á±Â ¶ ½Á Â Ã ½Á Â ¶ ½Á»Â Ã ´
. Select the correct
statement.
a)
The agent strictly prefers the lottery
Ä
Å
± Æ
Ä
Å
»
to the certain outcome
.
b)
The Bernoullian utility function
Ç¾ ¸ ¿ À
defined by
ÇÁ±Â ³ È
,
ÇÁ Â ³ µ
and
ÇÁ»Â ³ ·
represents the same preferences over lotteries as
½
.
c)
The agent strictly prefers the lottery
Ä
Å
Æ
Ä
Å
»
to the certain outcome
±
.
d)
The agent is risk averse.