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Game Theory · Nash equilibrium, dominance & mixing

12 questions · 22 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

Nash equilibrium, dominance & mixing

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Read the passage below, then answer Q1–Q2
(Choosing a route) Four people must drive from A to B at the same time. Two routes are available, one via X and one via Y (Refer to the left panel of following Figure). The roads from A to X, and from Y to B are both short and narrow; in each case, one car takes 6 minutes, and each additional car increases the travel time per car by 3 minutes. (If two cars drive from A to X, for example, each car takes 9 minutes.) The roads from A to Y, and from X to B are long and wide; on A to Y one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute; on X to B one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minutes. Formulate this situation as a strategic game and answer the given subquestions.
Q1MCQ2 Marks·Choose one option
Key ↓
Choose the correct alternative
1. AIn Nash equilibrium two people take each route
2. BFor the NE action profile, each person’s travel time is either 29.9 or 30 minutes
3. CBoth In Nash equilibrium two people take each route & For the NE action profile, each person’s travel time is either 29.9 or 30 minutes
4. DNone
Q2MCQ2 Marks·Choose one option
Key ↓
Now suppose that a relatively short, wide road is built from X to Y, giving each person four options for travel from A to B: A–X–B, A–Y–B, A–X–Y–B, and A–Y– X–B (As shown in the right panel of the given figure). Assume that a person who takes A–X–Y–B travels the A–X portion at the same time as someone who takes A–X–B, and the Y–B portion at the same time as someone who takes A–Y–B. (Think of there being constant flows of traffic.) On the road between X and Y, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Consider the Nash equilibrium in this new situation. Choose the correct alternative
1. AIn any Nash equilibrium, two persons take A–X–B, one person takes A–X–Y–B, and one person takes A–Y–B
2. BIn equilibrium profile, every person’s travel time increases compared to the case when new road was not there
3. CBoth In any Nash equilibrium, two persons take A–X–B, one person takes A–X–Y–B, and one person takes A–Y–B & In equilibrium profile, every person’s travel time increases compared to the case when new road was not there
4. DNone
Read the passage below, then answer Q3–Q4
An item is up for auction. Player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either 0, 1 or 2. If player i bids more than player j then i wins the good and pays his bid, while the loser does not pay. If both players bid the same amount, then a coin is tossed to determine who the winner is, who gets the good and pays his bid while the loser pays nothing. Formulate the game in matrix form and answer the given subquestions.
Q3MCQ2 Marks·Choose one option
Key ↓
Which player does not have strictly dominated strategy?
1. APlayer 1
2. BPlayer 2
3. CNone
Q4MCQ2 Marks·Choose one option
Key ↓
Which strategies survive Iterated Elimination of Strictly Dominated Strategy?
1. A(0, 0)
2. B(1, 1)
3. C(2, 2)
4. DNone
Read the passage below, then answer Q5–Q6
Consider the following normal form game and answer the given sub questions:
Q5MCQ2 Marks·Choose one option
Asked 2 times Key ↓
This game has
1. AA unique Nash equilibrium in pure strategy
2. BA unique Nash equilibrium in mixed strategy
3. CBoth are true
4. DNone is true
Q6NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q7–Q9
Based on the above data, answer the given subquestions.
Q7NAT2 Marks·Write the number
Asked 2 times Key ↓
How many pure strategy equilibria are there in this game?
Your answer:
Q8MCQ1 Mark·Choose one option
Asked 2 times Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE
Q9MCQ2 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

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q10–Q12
Based on the above data, answer the given subquestions.
Q10NAT1 Mark·Write the number
Asked 2 times Key ↓
How many pure strategy equilibria are there in this game?
Your answer:
Q11MCQ1 Mark·Choose one option
Asked 2 times Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE
Q12MCQ2 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

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1C

Q2B

Q3A

Q4C

Q5B

Q68

Q73

Q8B

Q9C

Q103

Q11B

Q12C

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