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Game Theory · Extensive form, SPE & repeated games

11 questions · 11 marks · 2 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

Extensive form, SPE & repeated games

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Read the passage below, then answer Q1–Q8
Consider a two-player game in which player 1 can choose A or B. The game ends if he chooses A while it continues to player 2 if he chooses B. Player 2 can either choose C or D, with the game ending after C and continuing again with player 1 after D. Player 1 then can choose E or F, and then the game ends after each of these choices.
Imagine that the payoffs following choice A by player 1 are (2, 0), following C by player 2 are (3, 1), following E by player 1 are (0, 0) and following F by player 1 are (1, 2)
Model this as an extensive form game and answer the given subquestions:
Q1MCQ1 Mark·Choose one option
Key ↓
This is a game of
1. APerfect information
2. BImperfect information
3. CNone
4. DCan’t be determined
Q2MCQ1 Mark·Choose one option
Key ↓
How many terminal nodes does this game have?
1. A3
2. B2
3. C4
4. D5
Q3MCQ1 Mark·Choose one option
Key ↓
How many information sets does this game have?
1. A2
2. B3
3. C4
4. D1
Q4MCQ1 Mark·Choose one option
Key ↓
How many pure strategies does player 1 have?
1. A1
2. B2
3. C3
4. D4
Q5MCQ1 Mark·Choose one option
Key ↓
How many pure strategies does player 2 have?
1. A1
2. B2
3. C3
4. D4
Q6MCQ1 Mark·Choose one option
Key ↓
How many pure strategy Nash equilibria does this game have?
1. A1
2. B2
3. C3
4. D4
Q7MCQ1 Mark·Choose one option
Key ↓
Which one of the Nash equilibria is also a subgame perfect equilibrium?
1. A(AE, D)
2. B(AF, D)
3. C(BE, C)
4. D(BF, C)
Q8MCQ1 Mark·Choose one option
Key ↓
No. of sub games this game has
1. A1
2. B2
3. C3
4. D4

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Read the passage below, then answer Q9–Q11
Each one of two political parties can choose to buy time on commercial radio shows to broadcast negative ad campaigns against their rival. These choices are made simultaneously. Due to government regulation, it is forbidden to buy more than 2 hours of negative campaign time, so that each party cannot choose an amount of negative campaigning above 2 hours. Given a pair of choices (a_1,a_2), the payoff of party i is given by the following function: v_i (a_1,a_2) = a_i − 2a_j + a_ia_j − (a_i)^2. Write the normal form representation of this game and answer the given sub-questions.
Q9MCQ1 Mark·Choose one option
Key ↓
Now assume that this game is repeated infinitely and the parties cooperate and sign a binding agreement on how much to campaign. What will be the payoff of each player in each stage game if they stick to this agreement
1. A-1.5
2. B1
3. C-1
4. D0
Q10MCQ1 Mark·Choose one option
Key ↓
Now assume that this game is repeated infinitely and the parties cooperate and sign a binding agreement on how much to campaign.
1. A
2. B
3. C
4. D
Q11MCQ1 Mark·Choose one option
Key ↓
Now assume that this game is repeated infinitely and the parties cooperate and sign a binding agreement on how much to campaign.
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1A

Q2C

Q3B

Q4D

Q5B

Q6C

Q7B

Q8C

Q9D

Q10B

Q11B

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