ms4023_2026T2_ET_FN.pdf
Game Theory and Strategy · End Term · May 2026 FN
← Course papers · Start practice / exam
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
A man goes bankrupt and his entire estate at the time of bankruptcy is worth 300 units. The man
has two creditors; one’s claim is 250 units, the other’s, 130 units. The division of the estate
between them is carried out according to the contested-garment principle.
Based on the above data, answer the given subquestions.
Creditor 1 with claim 250 units gets
210
170
250
125
A published solution is not available for this question yet.
Question 3 MCQ · 1.0 marks
A man goes bankrupt and his entire estate at the time of bankruptcy is worth 300 units. The man
has two creditors; one’s claim is 250 units, the other’s, 130 units. The division of the estate
between them is carried out according to the contested-garment principle.
Based on the above data, answer the given subquestions.
Creditor 2 with claim 130 units gets
130
100
90
65
A published solution is not available for this question yet.
Question 4 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 1 will be ________
A published solution is not available for this question yet.
Question 5 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 2 will be _________
A published solution is not available for this question yet.
Question 6 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 3 will be ________
A published solution is not available for this question yet.
Question 7 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 4 will be _________
A published solution is not available for this question yet.
Question 8 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 5 will be ________
A published solution is not available for this question yet.
Question 9 NAT · 0.5 marks
A cable TV station wants to connect six new customers to its network. The connections to the
network are described in the following tree graph:
[[IMAGE:57fd4efeccb118bb_3_2]]
Calculate the distribution of the costs among the six players if all six decide to connect to the
network.
Based on the above data, answer the given subquestions.
The cost to be paid by player 6 will be ________
A published solution is not available for this question yet.
Question 10 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
a = ______
A published solution is not available for this question yet.
Question 11 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
b = ______
A published solution is not available for this question yet.
Question 12 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
c = ______
A published solution is not available for this question yet.
Question 13 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
d = ______
A published solution is not available for this question yet.
Question 14 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
e = _____
A published solution is not available for this question yet.
Question 15 NAT · 0.5 marks
A game is split into two different games below. Supply the missing values.
[[IMAGE:57fd4efeccb118bb_5_3]]
Based on the above data, answer the given subquestions.
f = ______
A published solution is not available for this question yet.
Question 16 NAT · 1.0 marks
[[IMAGE:57fd4efeccb118bb_7_4]]
Based on the above data, answer the given subquestions.
S1 = ___________
A published solution is not available for this question yet.
Question 17 NAT · 1.0 marks
[[IMAGE:57fd4efeccb118bb_7_4]]
Based on the above data, answer the given subquestions.
S2 = ___________
A published solution is not available for this question yet.
Question 18 NAT · 1.0 marks
[[IMAGE:57fd4efeccb118bb_7_4]]
Based on the above data, answer the given subquestions.
S3 = ____________
A published solution is not available for this question yet.
Question 19 NAT · 1.0 marks
[[IMAGE:57fd4efeccb118bb_9_5]]
Based on the above data, answer the given subquestions.
What is the best response of roommate 2 if roommate 1 chooses t1=0?
t2 = ________
A published solution is not available for this question yet.
Question 20 NAT · 2.0 marks
[[IMAGE:57fd4efeccb118bb_9_5]]
Based on the above data, answer the given subquestions.
[[IMAGE:57fd4efeccb118bb_9_6]]
A published solution is not available for this question yet.
Question 21 NAT · 2.0 marks
Suppose that you receive a piece of e-mail whose subject line contains the phrase “check this out”
(a popular phrase among scammers). Based just on this and without looking at the sender or the
message content, what is the chance that the message is spam? Suppose that 40% of all your
mails are spam and the remaining 60% are emails you want to receive. Suppose that 1% of all
spam messages contain the phrase “check this out” in their subject lines, while 0.4% of all non-
spam messages contain this phrase.
Based on the above data, answer the given subquestions.
What is the total probability of having the phrase “check this out” in the subject line of an email?
A published solution is not available for this question yet.
Question 22 NAT · 2.0 marks
Suppose that you receive a piece of e-mail whose subject line contains the phrase “check this out”
(a popular phrase among scammers). Based just on this and without looking at the sender or the
message content, what is the chance that the message is spam? Suppose that 40% of all your
mails are spam and the remaining 60% are emails you want to receive. Suppose that 1% of all
spam messages contain the phrase “check this out” in their subject lines, while 0.4% of all non-
spam messages contain this phrase.
Based on the above data, answer the given subquestions.
What is the probability that the message is spam if the subject contains the phrase “check this
out”?
A published solution is not available for this question yet.
Question 23 MCQ · 1.0 marks
Given the following preference structure, find a stable matching system using the Gale–Shapley
algorithm when the men propose:
Women: A,B,C,D.
[[IMAGE:57fd4efeccb118bb_11_7]]
Men: a,b,c,d.
[[IMAGE:57fd4efeccb118bb_11_8]]
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 24 MCQ · 1.0 marks
Given the following preference structure, find a stable matching system using the Gale–Shapley
algorithm when the men propose:
Women: A,B,C,D.
[[IMAGE:57fd4efeccb118bb_11_7]]
Men: a,b,c,d.
[[IMAGE:57fd4efeccb118bb_11_8]]
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 25 MCQ · 1.0 marks
Given the following preference structure, find a stable matching system using the Gale–Shapley
algorithm when the men propose:
Women: A,B,C,D.
[[IMAGE:57fd4efeccb118bb_11_7]]
Men: a,b,c,d.
[[IMAGE:57fd4efeccb118bb_11_8]]
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 26 MCQ · 1.0 marks
Given the following preference structure, find a stable matching system using the Gale–Shapley
algorithm when the men propose:
Women: A,B,C,D.
[[IMAGE:57fd4efeccb118bb_11_7]]
Men: a,b,c,d.
[[IMAGE:57fd4efeccb118bb_11_8]]
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 27 MCQ · 1.0 marks
Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games.
This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see
what is offered. They both end up at one stand where the ancient board game “Chaturanga” is
offered in a second price auction. If they both bid the same, the winner is decided with the toss of
a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them
are of course very interested, nobody else cares about the old game and participates in the
auction. Mohan and Charan know each other well. In particular, they both know the willingness to
pay for the game of the other. Mohan is willing to pay ₹70000, while Charan’s maximum
willingness to pay is ₹90000. The only admissible bids are 50, 70, and 90 thousand of INR.
Represent the situation as a normal form game and answer the given subquestions:
There is no strictly dominated strategy for Mohan and Charan both.
True
False
A published solution is not available for this question yet.
Question 28 MCQ · 1.0 marks
Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games.
This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see
what is offered. They both end up at one stand where the ancient board game “Chaturanga” is
offered in a second price auction. If they both bid the same, the winner is decided with the toss of
a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them
are of course very interested, nobody else cares about the old game and participates in the
auction. Mohan and Charan know each other well. In particular, they both know the willingness to
pay for the game of the other. Mohan is willing to pay ₹70000, while Charan’s maximum
willingness to pay is ₹90000. The only admissible bids are 50, 70, and 90 thousand of INR.
Represent the situation as a normal form game and answer the given subquestions:
No. of Nash equilibria in pure strategies is
1
3
5
7
A published solution is not available for this question yet.
Question 29 MCQ · 1.0 marks
Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games.
This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see
what is offered. They both end up at one stand where the ancient board game “Chaturanga” is
offered in a second price auction. If they both bid the same, the winner is decided with the toss of
a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them
are of course very interested, nobody else cares about the old game and participates in the
auction. Mohan and Charan know each other well. In particular, they both know the willingness to
pay for the game of the other. Mohan is willing to pay ₹70000, while Charan’s maximum
willingness to pay is ₹90000. The only admissible bids are 50, 70, and 90 thousand of INR.
Represent the situation as a normal form game and answer the given subquestions:
For Mohan, playing 70000 weakly dominates playing 50000 or 90000.
True
False
A published solution is not available for this question yet.
Question 30 MCQ · 1.0 marks
Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games.
This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see
what is offered. They both end up at one stand where the ancient board game “Chaturanga” is
offered in a second price auction. If they both bid the same, the winner is decided with the toss of
a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them
are of course very interested, nobody else cares about the old game and participates in the
auction. Mohan and Charan know each other well. In particular, they both know the willingness to
pay for the game of the other. Mohan is willing to pay ₹70000, while Charan’s maximum
willingness to pay is ₹90000. The only admissible bids are 50, 70, and 90 thousand of INR.
Represent the situation as a normal form game and answer the given subquestions:
For Charan, playing 90000 weakly dominates playing 50000 or 70000.
True
False
A published solution is not available for this question yet.
Question 31 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1) = _____
A published solution is not available for this question yet.
Question 32 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(2) = _______
A published solution is not available for this question yet.
Question 33 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(3) = ________
A published solution is not available for this question yet.
Question 34 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1,3) = ________
A published solution is not available for this question yet.
Question 35 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1,4) = ________
A published solution is not available for this question yet.
Question 36 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(2,3) = _______
A published solution is not available for this question yet.
Question 37 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(2,4) = _______
A published solution is not available for this question yet.
Question 38 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(3,4) = _______
A published solution is not available for this question yet.
Question 39 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1,2,3) = ______
A published solution is not available for this question yet.
Question 40 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(2,3,4) = _______
A published solution is not available for this question yet.
Question 41 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1,3,4) =______
A published solution is not available for this question yet.
Question 42 NAT · 0.5 marks
A game v describes a four-player market in which there are two sellers and two buyers. Where the
first two players are potential sellers and the other two players are potential buyers. Each seller
has a good that he offers for sale and whose worth for him is $100. Each buyer wants to buy a
single good whose worth for him is $150. The potential buyers do not have a good like the one
offered for sale. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.
v(1,2,3,4) = _______
A published solution is not available for this question yet.
Question 43 MCQ · 1.0 marks
[[IMAGE:57fd4efeccb118bb_18_9]]
Based on the above data, answer the given subquestions.
For what values of CA and CB would there be a Nash equilibrium in which nobody learned the other
group’s language?
CA should be
[[IMAGE:57fd4efeccb118bb_18_10]]
[[IMAGE:57fd4efeccb118bb_18_11]]
[[IMAGE:57fd4efeccb118bb_18_12]]
[[IMAGE:57fd4efeccb118bb_18_13]]
A published solution is not available for this question yet.
Question 44 MCQ · 1.0 marks
[[IMAGE:57fd4efeccb118bb_18_9]]
Based on the above data, answer the given subquestions.
For what values of CA and CB would there be a Nash equilibrium in which nobody learned the other
group’s language?
CB should be
[[IMAGE:57fd4efeccb118bb_19_14]]
[[IMAGE:57fd4efeccb118bb_19_15]]
[[IMAGE:57fd4efeccb118bb_19_16]]
[[IMAGE:57fd4efeccb118bb_19_17]]
A published solution is not available for this question yet.
Question 45 MCQ · 2.0 marks
[[IMAGE:57fd4efeccb118bb_18_9]]
Based on the above data, answer the given subquestions.
An outcome is said to be socially efficient if it maximizes total benefits minus total costs. For what
values of CA and CB would it be socially efficient for type A’s to learn language B?
The condition on CA and CB should be
[[IMAGE:57fd4efeccb118bb_19_18]]
[[IMAGE:57fd4efeccb118bb_19_19]]
[[IMAGE:57fd4efeccb118bb_19_20]]
[[IMAGE:57fd4efeccb118bb_19_21]]
A published solution is not available for this question yet.
Question 46 MCQ · 2.0 marks
[[IMAGE:57fd4efeccb118bb_18_9]]
Based on the above data, answer the given subquestions.
For what values of CA and CB, would there be an equilibrium in which the type A’s learned
language B and the type B’s did not learn language A.
CA should be
[[IMAGE:57fd4efeccb118bb_20_22]]
[[IMAGE:57fd4efeccb118bb_20_23]]
[[IMAGE:57fd4efeccb118bb_20_24]]
[[IMAGE:57fd4efeccb118bb_20_25]]
A published solution is not available for this question yet.
Question 47 MCQ · 2.0 marks
[[IMAGE:57fd4efeccb118bb_18_9]]
Based on the above data, answer the given subquestions.
For what values of CA and CB, would there be a Nash equilibrium in which the type B's learned
language A and the type A’s did not learn language B.
CB should be
[[IMAGE:57fd4efeccb118bb_20_26]]
[[IMAGE:57fd4efeccb118bb_20_27]]
[[IMAGE:57fd4efeccb118bb_20_28]]
[[IMAGE:57fd4efeccb118bb_20_29]]
A published solution is not available for this question yet.
Question 48 MCQ · 1.0 marks
Three roommates need to vote on whether they will adopt a new rule and clean their room once a
week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the
current rule. Imagine that players 1 and 2 prefer the new rule while player 3 prefers the old rule.
Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then
player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form
game and answer the given subquestions.
No. of subgames in this game is
5
4
7
8
A published solution is not available for this question yet.
Question 49 MCQ · 1.0 marks
Three roommates need to vote on whether they will adopt a new rule and clean their room once a
week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the
current rule. Imagine that players 1 and 2 prefer the new rule while player 3 prefers the old rule.
Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then
player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form
game and answer the given subquestions.
No. of pure strategies player 1 has
2
3
4
6
A published solution is not available for this question yet.
Question 50 MCQ · 1.0 marks
Three roommates need to vote on whether they will adopt a new rule and clean their room once a
week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the
current rule. Imagine that players 1 and 2 prefer the new rule while player 3 prefers the old rule.
Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then
player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form
game and answer the given subquestions.
No. of pure strategies player 2 has
2
3
4
6
A published solution is not available for this question yet.
Question 51 MCQ · 1.0 marks
Three roommates need to vote on whether they will adopt a new rule and clean their room once a
week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the
current rule. Imagine that players 1 and 2 prefer the new rule while player 3 prefers the old rule.
Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then
player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form
game and answer the given subquestions.
No. of pure strategies player 3 has
4
6
12
16
A published solution is not available for this question yet.
Question 52 MCQ · 1.0 marks
Three roommates need to vote on whether they will adopt a new rule and clean their room once a
week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the
current rule. Imagine that players 1 and 2 prefer the new rule while player 3 prefers the old rule.
Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then
player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form
game and answer the given subquestions.
Imagine now that the players put their votes in a hat, so that the votes of earlier movers are not
observed by the later movers. No. of subgames in the new extensive form game will be
1
4
7
16
A published solution is not available for this question yet.