The IIT Madras BS Game Theory and Strategy (Game Theory) End Term paper sat on 21 Dec 2025, in the September 2025 term: 51 questions for 44 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
If an item is selected at random, the probability that the item is defective is ____________
Correct answer: 0.0375 (accepted within ±0.0025)
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ___________
Correct answer: 0.405 (accepted within ±0.005)
(A figure from the original paper is missing from the source site.)
(A figure from the original paper is missing from the source site.)
(A figure from the original paper is missing from the source site.)
None of these
Correct answer
(A figure from the original paper is missing from the source site.)
The maximum value of p to have buyers will be
(A figure from the original paper is missing from the source site.)
(A figure from the original paper is missing from the source site.)
Correct answer
Correct answer
increasing function of n
decreasing function of n
Correct answers
decreasing function of n
The fulfilled-expectations demand curve in this setting will be (consider (1-n)=m)
Correct answer
Correct answer: 5
True
False
Correct answer
True
If the unique, symmetric Nash equilibrium in pure strategy for this game is represented by
Correct answer: 10
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1)= _________________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(2)= ____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(3) =____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(4) = ____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,2) =____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,3)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,4)= ____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(2,3)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(2,4)= ____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(3,4)=____________
Correct answer: 0
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,2,3)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,2,4)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(2,3,4)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,3,4)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
v(1,2,3,4)= ____________
Correct answer: 1
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Consider following two statements and choose the correct alternative (I) This game has symmetrical players. (II) Players 1 and 2 are only symmetric players.
Only (I) is correct
Only (II) is correct
Both (I) and (II) are correct
None is correct
Correct answer
Only (I) is correct
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Consider following two statements and choose the correct alternative (I) This game has a null player. (II) Player 4 is null player.
Only (I) is correct
Only (II) is correct
Both (I) and (II) are correct
None is correct
Correct answer
Both (I) and (II) are correct
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Correct answer: 3
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Correct answer: 3
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Correct answer: 3
Given the game [61; 40, 40, 30, 10]. Write the game as a coalition function and find out symmetric and null players. Also, calculate Shapley-Shubik power index for the game.
Based on the above data, answer the given subquestions.
Correct answer: 0
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:
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 ___________
Correct answer: 7
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:
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 __________
Correct answer: 12
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:
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 ___________
Correct answer: 12
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:
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 ___________
Correct answer: 17
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:
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 ____________
Correct answer: 18
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:
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 _____________
Correct answer: 19
Six bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy.
Based on the above data, answer the given subquestions.
Optimal bid for a bidder with valuation 0.9 will be
0.48
0.65
0.5
0.75
Correct answer
0.75
Six bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy.
Based on the above data, answer the given subquestions.
The expected revenue of the seller in this auction scenario will be
4/5
5/7
2/3
2/5
Correct answer
5/7
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from that point onward. Every quarter that both firms operate yields each a loss equal to −1, and each quarter that a firm operates alone yields a payoff of 2. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (−1, 1) because both firms lose −1 in the first quarter and firm 2 gains 2 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter, and N denote exit next quarter.
Based on the above data, answer the given subquestions.
There are no strictly dominated strategies in this game.
True
False
Correct answer
True
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from that point onward. Every quarter that both firms operate yields each a loss equal to −1, and each quarter that a firm operates alone yields a payoff of 2. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (−1, 1) because both firms lose −1 in the first quarter and firm 2 gains 2 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter, and N denote exit next quarter.
Based on the above data, answer the given subquestions.
weakly dominated strategy in this game is
E
T
N
None
Correct answer
T
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from that point onward. Every quarter that both firms operate yields each a loss equal to −1, and each quarter that a firm operates alone yields a payoff of 2. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (−1, 1) because both firms lose −1 in the first quarter and firm 2 gains 2 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter, and N denote exit next quarter.
Based on the above data, answer the given subquestions.
Pure strategy Nash equilibria in this game are (More than one options correct)
(E, T)
(E, N)
(N, E)
(T, N)
Correct answers
(E, N)
(N, E)
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from that point onward. Every quarter that both firms operate yields each a loss equal to −1, and each quarter that a firm operates alone yields a payoff of 2. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (−1, 1) because both firms lose −1 in the first quarter and firm 2 gains 2 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter, and N denote exit next quarter.
Based on the above data, answer the given subquestions.
This game has unique mixed strategy equilibrium
True
False
Correct answer
True
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from that point onward. Every quarter that both firms operate yields each a loss equal to −1, and each quarter that a firm operates alone yields a payoff of 2. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (−1, 1) because both firms lose −1 in the first quarter and firm 2 gains 2 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter, and N denote exit next quarter.
Based on the above data, answer the given subquestions.
Correct answer: 2
A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 450 units, and the other’s claim, 250 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 450 units gets
350
300
200
250
Correct answer
350
A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 450 units, and the other’s claim, 250 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 250 units gets
150
300
200
250
Correct answer
150
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. Three advertisers are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
Total valuation of socially optimal allocation will be ___________
Correct answer: 40
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. Three advertisers are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
VCG price for slot a will be ___________
Correct answer: 15
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. Three advertisers are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
VCG price for slot b will be ____________
Correct answer: 5
Suppose 6 numbers are drawn independently from the uniform distribution on the interval [0, 1] and then sorted from smallest to largest. The expected value of the number in third position on the list is
5/6
3/7
1/2
1/3
Correct answer
3/7
Choose the correct alternative
A stable matching system is necessarily a system under which everyone is satisfied.
A matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
A stable matching system is necessarily a system under which everyone is satisfied & A matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
None of these
Correct answer
None of these
