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September 2025 term · Game Theory and Strategy · BSMS4023

Game Theory and Strategy Quiz 2: 23 November 2025 (September 2025 term)

The IIT Madras BS Game Theory and Strategy (Game Theory) Quiz 2 paper sat on 23 Nov 2025, in the September 2025 term: 25 questions for 25 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
25
Marks
25
Duration
120 min
MCQ
13
Written
4
Numerical
8
Take as mock testPractise with answers

Updated

Official paper: IIT M DEGREE AN EXAM QDB2 23 Nov 2025 NEW · No negative marking.

Question 1

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 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. A

    1/4

  2. B

    3/4

  3. C

    1/5

  4. D

    3/5

Show answer

Correct answer

  • A

    1/4

Question 1 on its own page

Question 2

+2 marksOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

What is the probability that the urn is red-majority if the first student draws a red ball?

  1. A

    2/5

  2. B

    3/5

  3. C

    3/4

  4. D

    1/4

Show answer

Correct answer

  • C

    3/4

Question 2 on its own page

Question 3

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

Should the first student guess the urn to be blue majority (in continuation to the previous question)?

  1. A

    Yes

  2. B

    No

Show answer

Correct answer

  • B

    No

Question 3 on its own page

Question 4

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

Now suppose, 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?

  1. A

    3/64

  2. B

    9/64

  3. C

    3/16

  4. D

    9/16

Show answer

Correct answer

  • A

    3/64

Question 4 on its own page

Question 5

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

Now suppose, 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. A

    3/64

  2. B

    9/64

  3. C

    3/16

  4. D

    9/16

Show answer

Correct answer

  • B

    9/64

Question 5 on its own page

Question 6

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

Now suppose, first three students draw the ball in the sequence (Red, Red, Blue).
What is the total probability of getting this sequence?

  1. A

    3/16

  2. B

    9/32

  3. C

    9/16

  4. D

    3/32

Show answer

Correct answer

  • D

    3/32

Question 6 on its own page

Question 7

+1 markOne correct option

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 blue ball 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 data,answer the given subquestions

Now suppose, first three students draw the ball in the sequence (Red, Red, Blue).
What is the probability of urn being red-majority in this scenario?

  1. A

    3/16

  2. B

    1/4

  3. C

    3/64

  4. D

    3/4

Show answer

Correct answer

  • D

    3/4

Question 7 on its own page

Question 8

+1 markOne correct option

Consider the following game matrix:

Player 1 \ Player 2SlowFast
Slow6,60,2
Fast2,01,1

Based on the data,answer the given subquestions

Choose the correct alternative

  1. A

    (Slow, Slow) is an NE

  2. B

    (Slow, Fast) is an NE

  3. C

    Both (Slow, Slow) is an NE & (Slow, Fast) is an NE

  4. D

    None of these

Show answer

Correct answer

  • A

    (Slow, Slow) is an NE

Question 8 on its own page

Question 9

+1 markOne correct option

Consider the following game matrix:

Player 1 \ Player 2SlowFast
Slow6,60,2
Fast2,01,1

Based on the data,answer the given subquestions

ESS in this game is

  1. A

    Slow

  2. B

    Fast

  3. C

    Both Slow & Fast

  4. D

    None of these

Show answer

Correct answer

  • C

    Both Slow & Fast

Question 9 on its own page

Question 10

+1 markWritten answer

Find a stable matching system for the following preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

ABCD
a1242
b2421
c3113
d4334

Men: a, b, c, d.

ABCD
a4213
b2134
c3142
d2413

In a stable matching when men propose to women, answer is case sensitive
Based on the data,answer the given subquestions

A will be matched with ________________

Show answer

Correct answer: b

Question 10 on its own page

Question 11

+1 markWritten answer

Find a stable matching system for the following preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

ABCD
a1242
b2421
c3113
d4334

Men: a, b, c, d.

ABCD
a4213
b2134
c3142
d2413

In a stable matching when men propose to women, answer is case sensitive
Based on the data,answer the given subquestions

B will be matched with ________________

Show answer

Correct answer: c

Question 11 on its own page

Question 12

+1 markWritten answer

Find a stable matching system for the following preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

ABCD
a1242
b2421
c3113
d4334

Men: a, b, c, d.

ABCD
a4213
b2134
c3142
d2413

In a stable matching when men propose to women, answer is case sensitive
Based on the data,answer the given subquestions

C will be matched with ________________

Show answer

Correct answer: d

Question 12 on its own page

Question 13

+1 markWritten answer

Find a stable matching system for the following preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

ABCD
a1242
b2421
c3113
d4334

Men: a, b, c, d.

ABCD
a4213
b2134
c3142
d2413

In a stable matching when men propose to women, answer is case sensitive
Based on the data,answer the given subquestions

D will be matched with ________________

Show answer

Correct answer: a

Question 13 on its own page

Question 14

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of a = ___________

Show answer

Correct answer: 3

Question 14 on its own page

Question 15

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of b = ___________

Show answer

Correct answer: 1.5

Question 15 on its own page

Question 16

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of c = ____________

Show answer

Correct answer: 1.5

Question 16 on its own page

Question 17

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of d = ___________

Show answer

Correct answer: 0

Question 17 on its own page

Question 18

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of p = ___________

Show answer

Correct answer: 0

Question 18 on its own page

Question 19

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of q = ___________

Show answer

Correct answer: 0.5

Question 19 on its own page

Question 20

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of r = ___________

Show answer

Correct answer: 0.5

Question 20 on its own page

Question 21

+0.5 marksNumerical answer

Based on the data,answer the given subquestions

Find out the value of t = ____________

Show answer

Correct answer: 1

Question 21 on its own page

Question 22

+2 marksOne correct option

Based on the data,answer the given subquestions

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

  1. A

    B

  2. B

    S

  3. C

    Either of the two

  4. D

    None of the two

Show answer

Correct answer

  • A

    B

Question 22 on its own page

Question 23

+2 marksOne correct option

Based on the data,answer the given subquestions

What is the Bayesian Nash equilibrium Strategy of both types of player 2 in this game?

  1. A

    (S, B)

  2. B

    (B, S)

  3. C

    (S, S)

  4. D

    (B, B)

Show answer

Correct answer

  • B

    (B, S)

Question 23 on its own page

Question 24

+1 markOne correct option

Unique NE of this game is

  1. A

    (Defect, Defect)

  2. B

    (Cooperate, Cooperate)

  3. C

    Both (Defect, Defect) & (Cooperate, Cooperate)

  4. D

    None of these

Show answer

Correct answer

  • A

    (Defect, Defect)

Question 24 on its own page

Question 25

+2 marksOne correct option

Suppose, this game is repeatedly played finite times

  1. A

    In the Last Period Cooperate is a dominant strategy irrespective of history of the game

  2. B

    In the Last Period Defect is a dominant strategy irrespective of history of the game

  3. C

    In the Last Period Cooperate is a dominant strategy for a particular game history

  4. 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 25 on its own page