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

39 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 (Forenoon)

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–Q2
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.
Q1NAT2 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:
Q2NAT2 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 Q3–Q4
Based on the above data, answer the given subquestions.
Q3NAT2 Marks·Write the number
Asked 4 times Key ↓
What is the best response of roommate 2 if roommate 1 chooses t_1 = 0? t_2 =________________
Your answer:
Q4NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q5–Q12
A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.
Q5NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q6NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q7NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q8NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q9NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q10NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q11NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q12NAT0.5 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q13–Q18
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q13MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q14MCQ1 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
Q15MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q16MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q17MSQ1 Mark·Choose all correct options
Asked 2 times Key ↓
p(n^e,n) is _____________ (more than one options are correct)
1. Aincreasing function of n
2. Bdecreasing function of n
3. Cdecreasing function of n^e
4. Dincreasing function of n^e
Q18MCQ1 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 Q19–Q22
Calculate the Shapley value of the following game using the procedure for dissolving a partnership
Based on the above data, answer the given subquestions.
Q19NAT1.5 Marks·Write the number
Asked 7 times Key ↓
S_1 = ________________
Your answer:
Q20NAT1.5 Marks·Write the number
Asked 7 times Key ↓
S_2 = ________________
Your answer:
Q21NAT1.5 Marks·Write the number
Asked 7 times Key ↓
S_3 = ________________
Your answer:
Q22NAT1.5 Marks·Write the number
Asked 7 times Key ↓
S_4 = ________________
Your answer:
Read the passage below, then answer Q23–Q25
Based on the above data, answer the given subquestions.
Q23NAT2 Marks·Write the number
Asked 2 times Key ↓
How many pure strategy equilibria are there in this game?
Your answer:
Q24MCQ1 Mark·Choose one option
Asked 2 times Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE
Q25MCQ2 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 Q26–Q28
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.
Q26NAT1 Mark·Write the number
Asked 6 times Key ↓
The cost to be paid by player 1 will be ______________
Your answer:
Q27NAT1 Mark·Write the number
Asked 6 times Key ↓
The cost to be paid by player 2 will be _________________
Your answer:
Q28NAT1 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 Q29–Q30
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:
Q29MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Optimal bid for a bidder with valuation 0.75 will be
1. A0.7
2. B0.6
3. C0.5
4. D0.75
Q30MCQ2 Marks·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
Read the passage below, then answer Q31–Q33
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.
Q31NAT1 Mark·Write the number
Asked 2 times Key ↓
Total valuation of socially optimal allocation will be ____________
Your answer:
Q32NAT1 Mark·Write the number
Asked 4 times Key ↓
VCG price for slot a will be _________
Your answer:
Q33NAT1 Mark·Write the number
Asked 4 times Key ↓
VCG price for slot b will be _________
Your answer:
Read the passage below, then answer Q34–Q35
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.
Q34NAT1 Mark·Write the number
Asked 4 times Key ↓
Creditor 1 with claim 400 units gets
Your answer:
Q35NAT1 Mark·Write the number
Asked 4 times Key ↓
Creditor 2 with claim 300 units gets
Your answer:
Q36MCQ2 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
Q37MCQ1 Mark·Choose one option
Asked 3 times Key ↓
In weighted majority game [7; 1, 4, 3, 5]
1. APlayer 1 is null player
2. BPlayer 2 is null player
3. CPlayer 3 is null player
4. DPlayer 4 is null player
Q38MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Consider following two statements: 1. Crowd can 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 sometimes produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth 1 & 2
4. DNone
Q39MCQ1 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

Q10.035 to 0.04

Q20.4 to 0.405

Q35

Q410

Q5200

Q60

Q70

Q80

Q90

Q10280

Q11300

Q12300

Q13B

Q14A

Q15C

Q16D

Q17B, D

Q18D

Q1974

Q2030

Q2162

Q2274

Q233

Q24B

Q25C

Q268

Q2730

Q2832

Q29B

Q30C

Q3140

Q3215

Q335

Q34300

Q35200

Q36D

Q37A

Q38C

Q39D

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