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Game Theory · End Term · 31 Aug 2025 (Afternoon)

37 questions · 45 marks · 90 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

End Term · 31 Aug 2025 (Afternoon)

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Read the passage below, then answer Q1–Q6
Enter the coalition function for the game [61;40,40,30,10] and answer the given sub-questions:
Q1NAT1 Mark·Write the number
Key ↓
How many symmetric players are in this game: _______________
Your answer:
Q2NAT1 Mark·Write the number
Asked 3 times Key ↓
Which player is the null player in this game? ____________
Your answer:
Q3NAT1 Mark·Write the number
Key ↓
Your answer:
Q4NAT1 Mark·Write the number
Key ↓
Your answer:
Q5NAT1 Mark·Write the number
Key ↓
Your answer:
Q6NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q7–Q12
Based on the above data, answer the given subquestions.
Q7MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q8MCQ1 Mark·Choose one option
Asked 2 times Key ↓
The maximum value of p to have buyers will be
1. A
2. B
3. C
4. D
Q9MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q10MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q11MSQ1 Mark·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q12MCQ1 Mark·Choose one option
Asked 2 times Key ↓
The fulfilled-expectations demand curve in this setting will be
1. A
2. B
3. C
4. D
Read the passage below, then answer Q13–Q15
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. There are three advertisers who 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.
Q13NAT2 Marks·Write the number
Asked 2 times Key ↓
Total valuation of socially optimal allocation will be ___________
Your answer:
Q14NAT2 Marks·Write the number
Asked 4 times Key ↓
VCG price for slot a will be ___________
Your answer:
Q15NAT2 Marks·Write the number
Asked 4 times Key ↓
VCG price for slot b will be __________
Your answer:
Read the passage below, then answer Q16–Q18
Calculate the Shapley value of the following game and answer the given subquestions.
Q16NAT1 Mark·Write the number
Asked 7 times Key ↓
S_1 = _____________
Your answer:
Q17NAT1 Mark·Write the number
Asked 7 times Key ↓
S_2 = _____________
Your answer:
Q18NAT1 Mark·Write the number
Asked 7 times Key ↓
S_3 = _____________
Your answer:
Read the passage below, then answer Q19–Q21
A cable TV station wants to connect three 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 three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions.
Q19NAT1 Mark·Write the number
Asked 6 times Key ↓
The cost to be paid by player 1 will be _____________
Your answer:
Q20NAT1 Mark·Write the number
Asked 6 times Key ↓
The cost to be paid by player 2 will be ____________
Your answer:
Q21NAT1 Mark·Write the number
Asked 6 times Key ↓
The cost to be paid by player 3 will be ____________
Your answer:
Read the passage below, then answer Q22–Q23
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.
Q22NAT2 Marks·Write the number
Asked 3 times Key ↓
If an item is selected at random, the probability that the item is defective is ______________
Your answer:
Q23NAT2 Marks·Write the number
Asked 4 times Key ↓
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ____________
Your answer:
Read the passage below, then answer Q24–Q26
Based on the above data, answer the given subquestions.
Q24NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q25NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Q26NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q27–Q29
Based on the above data, answer the given subquestions.
Q27NAT1 Mark·Write the number
Asked 2 times Key ↓
How many pure strategy equilibria are there in this game?
Your answer:
Q28MCQ1 Mark·Choose one option
Asked 2 times Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE
Q29MCQ2 Marks·Choose one option
Asked 2 times Key ↓
There is a symmetric mixed strategy equilibrium where all three players enter with the same probability (say p). Find the value of p
1. A1/5
2. B3/5
3. C4/5
4. D2/5
Read the passage below, then answer Q30–Q31
A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 400 units, and the other’s claim, 300 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.
Q30NAT1 Mark·Write the number
Asked 4 times Key ↓
Creditor 1 with claim 400 units gets
Your answer:
Q31NAT1 Mark·Write the number
Asked 4 times Key ↓
Creditor 2 with claim 300 units gets
Your answer:
Read the passage below, then answer Q32–Q33
Five 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 answer the given sub-questions:
Q32MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Optimal bid for a bidder with valuation 0.6 will be
1. A0.4
2. B0.48
3. C0.5
4. D0.55
Q33MCQ1 Mark·Choose one option
Asked 2 times Key ↓
The expected revenue of the seller in this auction scenario will be
1. A4/5
2. B3/5
3. C2/3
4. D2/5
Q34MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Suppose 5 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 second position on the list is
1. A5/6
2. B2/3
3. C1/2
4. D1/3
Q35MCQ1 Mark·Choose one option
Asked 3 times Key ↓
In weighted majority game [7; 5, 1, 3, 4]
1. APlayer 1 is null player
2. BPlayer 2 is null player
3. CPlayer 3 is null player
4. DPlayer 4 is null player
Q36MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Consider following two statements: 1. Crowd can be never be wrong even if everyone in the crowd is rational and everyone takes the same action. 2. Aggregate behaviour of many people with limited information can never produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth the Only 1 & Only 2
4. DNone
Q37MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Choose the correct alternative
1. AA stable matching system is necessarily a system under which everyone is satisfied.
2. BA matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
3. CBoth 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.
4. DNone

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q13

Q24

Q33

Q43

Q53

Q60

Q7B

Q8A

Q9C

Q10D

Q11B, D

Q12D

Q1340

Q1415

Q155

Q165

Q175

Q180

Q196

Q2030

Q2130

Q220.035 to 0.04

Q230.4 to 0.405

Q2450

Q2566.5 to 67

Q264444

Q273

Q28B

Q29C

Q30300

Q31200

Q32B

Q33C

Q34D

Q35B

Q36D

Q37D

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.