ms4023_2026T2_Q2_NA.pdf
Game Theory and Strategy · Quiz 2 · May 2026
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Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.
Question 2 MCQ · 1.0 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Unique NE of this game is
(Defect, Defect )
(Cooperate, Cooperate )
Both
None
A published solution is not available for this question yet.
Question 3 MCQ · 1.0 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Suppose, this game is repeatedly played finite times
In the last period Cooperate is a dominant strategy irrespective of history of
the game
In the last period Defect is a dominant strategy irrespective of history of the
game
In the last period Cooperate is a dominant strategy for a particular game
history
In the last period Defect is a dominant strategy for a particular game history
A published solution is not available for this question yet.
Question 4 NAT · 0.5 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Suppose, this game is repeatedly played for 2 times and in the first period, if both players choose
their dominant strategy. Derive the payoff matrix for second period and find out the value of
following unknowns that represent payoff at the end of second period:
[[IMAGE:afe745f7467cc7e4_3_3]]
j= ____________
A published solution is not available for this question yet.
Question 5 NAT · 0.5 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Suppose, this game is repeatedly played for 2 times and in the first period, if both players choose
their dominant strategy. Derive the payoff matrix for second period and find out the value of
following unknowns that represent payoff at the end of second period:
[[IMAGE:afe745f7467cc7e4_4_4]]
l=____________
A published solution is not available for this question yet.
Question 6 NAT · 0.5 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Suppose, this game is repeatedly played for 2 times and in the first period, if both players choose
their dominant strategy. Derive the payoff matrix for second period and find out the value of
following unknowns that represent payoff at the end of second period:
[[IMAGE:afe745f7467cc7e4_4_5]]
m=____________
A published solution is not available for this question yet.
Question 7 NAT · 0.5 marks
Consider the following prisoners’ dilemma game and answer the given subquestions
[[IMAGE:afe745f7467cc7e4_2_2]]
Suppose, this game is repeatedly played for 2 times and in the first period, if both players choose
their dominant strategy. Derive the payoff matrix for second period and find out the value of
following unknowns that represent payoff at the end of second period:
[[IMAGE:afe745f7467cc7e4_5_6]]
r =____________
A published solution is not available for this question yet.
Question 8 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
a = __________
A published solution is not available for this question yet.
Question 9 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
b =__________
A published solution is not available for this question yet.
Question 10 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
c =__________
A published solution is not available for this question yet.
Question 11 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
d =__________
A published solution is not available for this question yet.
Question 12 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
p =__________
A published solution is not available for this question yet.
Question 13 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
q =__________
A published solution is not available for this question yet.
Question 14 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
r =__________
A published solution is not available for this question yet.
Question 15 NAT · 0.5 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
Find out the value of following unknown:
t =__________
A published solution is not available for this question yet.
Question 16 MCQ · 1.0 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
What is the Bayesian Nash equilibrium Strategy of player 1 in this game?
B
S
Either of the two
None
A published solution is not available for this question yet.
Question 17 MCQ · 1.0 marks
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed
in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to
avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1
thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2
wants to avoid her. The situation is depicted in the following matrix of a static game with
incomplete information:
[[IMAGE:afe745f7467cc7e4_6_7]]
With the help of this game matrix, we may come up with the following table depicting expected
payoff of player 1 corresponding to different actions of both types of player 2.
[[IMAGE:afe745f7467cc7e4_6_8]]
Based on the above data, answer the given subquestions.
What is the Bayesian Nash equilibrium Strategy of both types of player 2 in this game?
(B,S)
(B,B)
(S,B)
(S,S)
A published solution is not available for this question yet.
Question 18 MCQ · 1.0 marks
Consider the following game matrix:
[[IMAGE:afe745f7467cc7e4_10_9]]
Based on the above data, answer the given subquestions.
Choose the correct alternative
(Slow, Slow) is an NE
(Slow, Fast) is an NE
Both
None
A published solution is not available for this question yet.
Question 19 MCQ · 1.0 marks
Consider the following game matrix:
[[IMAGE:afe745f7467cc7e4_10_9]]
Based on the above data, answer the given subquestions.
ESS in this game is
Slow
Fast
Both
None
A published solution is not available for this question yet.
Question 20 MCQ · 0.5 marks
Given the following preference structure, find a stable matching system using the Gale- Shapley
algorithm when the men propose.
[[IMAGE:afe745f7467cc7e4_11_10]]
Based on the above data, answer the given subquestions.
Ms. A will be paired with
a
c
d
b
A published solution is not available for this question yet.
Question 21 MCQ · 0.5 marks
Given the following preference structure, find a stable matching system using the Gale- Shapley
algorithm when the men propose.
[[IMAGE:afe745f7467cc7e4_11_10]]
Based on the above data, answer the given subquestions.
Ms. B will be paired with
b
c
a
d
A published solution is not available for this question yet.
Question 22 MCQ · 0.5 marks
Given the following preference structure, find a stable matching system using the Gale- Shapley
algorithm when the men propose.
[[IMAGE:afe745f7467cc7e4_11_10]]
Based on the above data, answer the given subquestions.
Ms. C will be paired with
b
d
c
a
A published solution is not available for this question yet.
Question 23 MCQ · 0.5 marks
Given the following preference structure, find a stable matching system using the Gale- Shapley
algorithm when the men propose.
[[IMAGE:afe745f7467cc7e4_11_10]]
Based on the above data, answer the given subquestions.
Ms. D will be paired with
a
d
b
c
A published solution is not available for this question yet.
Question 24 MCQ · 1.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Suppose one ball is picked from the red majority urn. What is the probability that the ball is blue?
1/3
1/4
1/2
2/3
A published solution is not available for this question yet.
Question 25 MCQ · 2.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
What is the probability that the urn is red majority if the first student draws a red ball?
2/4
1/3
2/3
1/4
A published solution is not available for this question yet.
Question 26 MCQ · 1.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, the first three students draw the ball in the sequence (Red, Red, Blue).
What is the probability of getting this sequence if the urn is a blue majority urn?
2/27
4/27
1/27
6/27
A published solution is not available for this question yet.
Question 27 MCQ · 1.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, the first three students draw the ball in the sequence (Red, Red, Blue).
What is the probability of getting this sequence if the urn is a red majority urn?
1/27
4/27
6/27
2/27
A published solution is not available for this question yet.
Question 28 MCQ · 2.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, the first three students draw the ball in the sequence (Red, Red, Blue).
What is the total probability of getting this sequence?
1/27
1/9
4/27
4/9
A published solution is not available for this question yet.
Question 29 MCQ · 1.0 marks
Consider the example of cascade discussed in the lecture but with a modification that now the urn
is containing either 4 blue balls and 2 red balls or 4 red balls and 2 blue balls with equal
probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority
urn. We assume everyone hears what the previous individuals report and get their own private
signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, the first three students draw the ball in the sequence (Red, Red, Blue).
What is the probability of the urn being red majority in this scenario?
3/6
1/3
2/3
1/6
A published solution is not available for this question yet.
Question 30 MCQ · 1.0 marks
**Grim Trigger:** Consider the infinitely repeated game with discount factor δ<1 of the following
variant of the Prisoner’s Dilemma:
[[IMAGE:afe745f7467cc7e4_14_11]]
Based on the above data, answer the given subquestions.
Unique NE of this game is
(T,L)
(B,R)
(M,C)
None
A published solution is not available for this question yet.
Question 31 MCQ · 1.0 marks
**Grim Trigger:** Consider the infinitely repeated game with discount factor δ<1 of the following
variant of the Prisoner’s Dilemma:
[[IMAGE:afe745f7467cc7e4_14_11]]
Based on the above data, answer the given subquestions.
For which values of the discount factor δ can the players support the pair of actions (M,C) played in
every period?
(δ ≥ 1/5)
(δ ≥ 1/3)
(δ ≥ 3/7)
(δ ≥ 1/2)
A published solution is not available for this question yet.
Question 32 MCQ · 1.0 marks
**Grim Trigger:** Consider the infinitely repeated game with discount factor δ<1 of the following
variant of the Prisoner’s Dilemma:
[[IMAGE:afe745f7467cc7e4_14_11]]
Based on the above data, answer the given subquestions.
For which values of the discount factor δ can the players support the pair of actions (T,L) played in
every period?
(δ ≥ 1/7)
(δ ≥ 0)
(δ ≥ 1/4)
(δ ≥ 1/2)
A published solution is not available for this question yet.