Consider the following prisoners’ dilemma game and answer the given subquestions Figure from the passage in the original paper Suppose, this game is repeatedly played finite times

(B) In the last period Defect is a dominant strategy irrespective of history of the game

(A) In the last period Cooperate is a dominant strategy irrespective of history of the game

(C) In the last period Cooperate is a dominant strategy for a particular game history

(D) In the last period Defect is a dominant strategy for a particular game history

Game Theory Quiz 2 PYQ May 2026: 16 Aug 2026 · IITM BS

Question 1

+1 markOne correct option

Consider the following prisoners’ dilemma game and answer the given subquestions

Unique NE of this game is

A
(Defect, Defect )
B
(Cooperate, Cooperate )
C
Both
D
None

Show answer

Correct answer

A
(Defect, Defect )

Question 1 on its own page

Question 2

+1 markOne correct option

Consider the following prisoners’ dilemma game and answer the given subquestions

Suppose, this game is repeatedly played finite times

A
In the last period Cooperate is a dominant strategy irrespective of history of the game
B
In the last period Defect is a dominant strategy irrespective of history of the game
C
In the last period Cooperate is a dominant strategy for a particular game history
D
In the last period Defect is a dominant strategy for a particular game history

Show answer

Correct answer

B
In the last period Defect is a dominant strategy irrespective of history of the game

Question 2 on its own page

Question 3

+0.5 marksNumerical answer

Consider the following prisoners’ dilemma game and answer the given subquestions

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:

j= ____________

Show answer

Correct answer: 7

Question 3 on its own page

Question 4

+0.5 marksNumerical answer

Consider the following prisoners’ dilemma game and answer the given subquestions

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:

l=____________

Show answer

Correct answer: 4

Question 4 on its own page

Question 5

+0.5 marksNumerical answer

Consider the following prisoners’ dilemma game and answer the given subquestions

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:

m=____________

Show answer

Correct answer: 8

Question 5 on its own page

Question 6

+0.5 marksNumerical answer

Consider the following prisoners’ dilemma game and answer the given subquestions

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:

r =____________

Show answer

Correct answer: 6

Question 6 on its own page

Question 7

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: a = __________

Show answer

Correct answer: 1

Question 7 on its own page

Question 8

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: b =__________

Show answer

Correct answer: 0.5

Question 8 on its own page

Question 9

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: c =__________

Show answer

Correct answer: 0.5

Question 9 on its own page

Question 10

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: d =__________

Show answer

Correct answer: 0

Question 10 on its own page

Question 11

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: p =__________

Show answer

Correct answer: 0

Question 11 on its own page

Question 12

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: q =__________

Show answer

Correct answer: 1

Question 12 on its own page

Question 13

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: r =__________

Show answer

Correct answer: 1

Question 13 on its own page

Question 14

+0.5 marksNumerical answer

(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:

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.

Based on the above data, answer the given subquestions.

Find out the value of following unknown: t =__________

Show answer

Correct answer: 2

Question 14 on its own page

Question 15

+1 markOne correct option

(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:

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.

Based on the above data, answer the given subquestions.

What is the Bayesian Nash equilibrium Strategy of player 1 in this game?

A
B
B
S
C
Either of the two
D
None

Show answer

Correct answer

B
S

Question 15 on its own page

Question 16

+1 markOne correct option

(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:

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.

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?

A
(B,S)
B
(B,B)
C
(S,B)
D
(S,S)

Show answer

Correct answer

C
(S,B)

Question 16 on its own page

Question 17

+1 markOne correct option

Consider the following game matrix:

Based on the above data, answer the given subquestions.

Choose the correct alternative

A
(Slow, Slow) is an NE
B
(Slow, Fast) is an NE
C
Both
D
None

Show answer

Correct answer

A
(Slow, Slow) is an NE

Question 17 on its own page

Question 18

+1 markOne correct option

Consider the following game matrix:

Based on the above data, answer the given subquestions.

ESS in this game is

A
Slow
B
Fast
C
Both
D
None

Show answer

Correct answer

C
Both

Question 18 on its own page

Question 19

+0.5 marksOne correct option

Given the following preference structure, find a stable matching system using the Gale- Shapley algorithm when the men propose.

Based on the above data, answer the given subquestions.

Ms. A will be paired with

A
a
B
c
C
d
D
b

Show answer

Correct answer

B
c

Question 19 on its own page

Question 20

+0.5 marksOne correct option

Given the following preference structure, find a stable matching system using the Gale- Shapley algorithm when the men propose.

Based on the above data, answer the given subquestions.

Ms. B will be paired with

A
b
B
c
C
a
D
d

Show answer

Correct answer

C
a

Question 20 on its own page

Question 21

+0.5 marksOne correct option

Given the following preference structure, find a stable matching system using the Gale- Shapley algorithm when the men propose.

Based on the above data, answer the given subquestions.

Ms. C will be paired with

A
b
B
d
C
c
D
a

Show answer

Correct answer

A
b

Question 21 on its own page

Question 22

+0.5 marksOne correct option

Given the following preference structure, find a stable matching system using the Gale- Shapley algorithm when the men propose.

Based on the above data, answer the given subquestions.

Ms. D will be paired with

A
a
B
d
C
b
D
c

Show answer

Correct answer

B
d

Question 22 on its own page

Question 23

+1 markOne correct option

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?

A
1/3
B
1/4
C
1/2
D
2/3

Show answer

Correct answer

A
1/3

Question 23 on its own page

Question 24

+2 marksOne correct option

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?

A
2/4
B
1/3
C
2/3
D
1/4

Show answer

Correct answer

C
2/3

Question 24 on its own page

Question 25

+1 markOne correct option

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?

A
2/27
B
4/27
C
1/27
D
6/27

Show answer

Correct answer

A
2/27

Question 25 on its own page

Question 26

+1 markOne correct option

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?

A
1/27
B
4/27
C
6/27
D
2/27

Show answer

Correct answer

B
4/27

Question 26 on its own page

Question 27

+2 marksOne correct option

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?

A
1/27
B
1/9
C
4/27
D
4/9

Show answer

Correct answer

B
1/9

Question 27 on its own page

Question 28

+1 markOne correct option

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?

A
3/6
B
1/3
C
2/3
D
1/6

Show answer

Correct answer

C
2/3

Question 28 on its own page

Question 29

+1 markOne correct option

Grim Trigger: Consider the infinitely repeated game with discount factor δ<1 of the following variant of the Prisoner’s Dilemma:

Based on the above data, answer the given subquestions.

Unique NE of this game is

A
(T,L)
B
(B,R)
C
(M,C)
D
None

Show answer

Correct answer

B
(B,R)

Question 29 on its own page

Question 30

+1 markOne correct option

Grim Trigger: Consider the infinitely repeated game with discount factor δ<1 of the following variant of the Prisoner’s Dilemma:

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?

A
(δ ≥ 1/5)
B
(δ ≥ 1/3)
C
(δ ≥ 3/7)
D
(δ ≥ 1/2)

Show answer

Correct answer

A
(δ ≥ 1/5)

Question 30 on its own page

Question 31

+1 markOne correct option

Grim Trigger: Consider the infinitely repeated game with discount factor δ<1 of the following variant of the Prisoner’s Dilemma:

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?

A
(δ ≥ 1/7)
B
(δ ≥ 0)
C
(δ ≥ 1/4)
D
(δ ≥ 1/2)

Show answer

Correct answer

C
(δ ≥ 1/4)

Question 31 on its own page