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Game Theory · Auctions & VCG pricing

12 questions · 18 marks · 2 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

Auctions & VCG pricing

Official Paper

Examination Instructions & Guidelines

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

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q1–Q2
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:
Q1MCQ1 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
Q2MCQ2 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 Q3–Q5
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.
Q3NAT1 Mark·Write the number
Asked 2 times Key ↓
Total valuation of socially optimal allocation will be ____________
Your answer:
Q4NAT1 Mark·Write the number
Asked 4 times Key ↓
VCG price for slot a will be _________
Your answer:
Q5NAT1 Mark·Write the number
Asked 4 times Key ↓
VCG price for slot b will be _________
Your answer:
Q6MCQ2 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

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q7–Q9
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.
Q7NAT2 Marks·Write the number
Asked 2 times Key ↓
Total valuation of socially optimal allocation will be ___________
Your answer:
Q8NAT2 Marks·Write the number
Asked 4 times Key ↓
VCG price for slot a will be ___________
Your answer:
Q9NAT2 Marks·Write the number
Asked 4 times Key ↓
VCG price for slot b will be __________
Your answer:
Read the passage below, then answer Q10–Q11
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:
Q10MCQ1 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
Q11MCQ1 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
Q12MCQ2 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

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1B

Q2C

Q340

Q415

Q55

Q6D

Q740

Q815

Q95

Q10B

Q11C

Q12D

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