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Unformatted text preview: Name:_____________________________ SID:_______________________ Tutor’s Name:_______________________ Tutorial Day & Time:_________________ SCHOOL OF ECONOMICS
ECONOMICS 2112
GAME THEORY AND BUSINESS STRATEGY
S1 2011
MIDTERM EXAM This exam comprises of 12 pages including this cover page.
There are 10 questions. Answer all 10.
Questions answered correctly are worth 3 marks.
Questions answered incorrectly are worth 1 mark.
Questions not answered are worth 0 mark.
Total time allowed: 60 minutes
Report your Student ID number (SID) at the top of each page.
Any evidence of dishonesty will be punished by failure and reported to the appropriate
authority 1 SID:_________________________ 1. Consider the following threeplayer game: L
C
R
1,2,2 0,3,2 1,2,9
2,1,7 ,1,0 2,2,1 T
B X For which values of
a)
b)
c)
d) and and is the strategy T
B L
C
R
0,3,0 ,3,1 1,2,2
2,1,2 3,1,4 2,2,3
Y weakly dominated but not strictly dominated? .
.
.
. 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
and suppose that an agent’s preferences are characterized by a Bernoullian
utility function
that satisfies
. Select the correct
statement.
a) The agent strictly prefers the lottery
to the certain outcome .
b) The Bernoullian utility function
defined by
,
represents the same preferences over lotteries as .
c) The agent strictly prefers the lottery
to the certain outcome .
d) The agent is risk averse. and 2 SID:_________________________ 4. Consider the game:
L
3,3
2,2
1,0 T
M
B C
2,2
2,2
1,1 R
0,1
1,1
1,1 Select the correct statement:
a) ,
,
are the Nash equilibria in pure strategies of the game. The
unique equilibrium in mixed strategies is
.
b)
is an equilibrium in dominant strategies.
c)
,
,
,
, and
are all the Nash
equilibria o f the game.
d) This game has three Nash equilibria, of which only two are admissible (i.e.,
undominated). 5. Given the following game:
L
6,2
1,1 L
7,2
4,0 T
B R
1,1
2,6 R
4,0
5,6 What is the set of Nash equilibria?
a)
b)
c)
d) .
.
.
. 6. Given the following game: T
B What is the set of Nash equilibria?
a)
b)
c)
d) .
.
.
.
3 SID:_________________________ 7. Given the following game:
L
5,5
9,2 T
B R
7,3
2,8 Select the wrong statement:
a) T and R are the players’ pure Minmax strategies.
b)
is the Row player’s Nash equilibrium strategy and
is the Column
player’ Nash equilibrium strategy.
c) For this type of game, the players’ mixed Minmax strategies are the same as their
Nash equilibrium mixed strategies.
d)
is the Row player’s mixed Minmax strategy and
is the Column
player’ mixed Minmax strategy.
8. Given the following game: T
B L
7,2
4,0 R
4,0
5,6 RR
7,1
3,2 Select the correct statement:
a) The strategy RR is weakly dominated but not strictly dominated.
b) The set of Nash equilibria is
.
c) The set of Nash equilibria is the same in Question 6.
d)
is the welfaremaximising Nash equilibrium because it maximizes the sum of
the payoffs.
9. Select the correct statement:
a)
b)
c)
d) If
is a dominated strategy then either A or B is also a dominated strategy.
An admissible (i.e., undominated) equilibrium must be a strict equilibrium.
If
is a dominated strategy then
is also a dominated strategy.
In every game, each player has a mixed strategy that is a dominant strategy. 10. Consider a normal form game
strategy profile
a)
b)
c)
d) For each
For each
For each
For each , . Select the wrong alternative. A
is a Nash equilibrium if: is a best response against
and every
,
and every
,
and every
, .
.
.
.
4 ...
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This note was uploaded on 06/19/2011 for the course ECON 2112 taught by Professor Arghyaghosh during the One '10 term at University of New South Wales.
 One '10
 ARGHYAGHOSH
 Game Theory

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