The IIT Madras BS Game Theory and Strategy (Game Theory) Quiz 2 paper sat on 3 Aug 2025, in the May 2025 term, set QDD2: 24 questions for 25 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
(Bayesian Game) Consider a two-player game in which the payoffs, which depend on , and actions are as in the following table:
Where . Player 2 knows exactly what value has, whereas player 1 doesn't know.
Based on the above data, answer the given subquestions.
Under Bayesian Nash Eq., player 1 will play
U
D
Correct answer
U
(Bayesian Game) Consider a two-player game in which the payoffs, which depend on , and actions are as in the following table:
Where . Player 2 knows exactly what value has, whereas player 1 doesn't know.
Based on the above data, answer the given subquestions.
Under Bayesian Nash Eq., player 2, who knows that θ = 0 will play
L
R
Correct answer
R
(Bayesian Game) Consider a two-player game in which the payoffs, which depend on , and actions are as in the following table:
Where . Player 2 knows exactly what value has, whereas player 1 doesn't know.
Based on the above data, answer the given subquestions.
Under Bayesian Nash Eq., player 2, who knows that θ = 1 will play
L
R
Correct answer
L
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
If player 1 chooses 2 hours as his action, the best response of player 2 will be
1.5
1
1.25
0
Correct answer
1.5
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
How much negative campaign time will each player choose under a symmetric and unique Nash equilibrium?
1.5
1
1.25
0
Correct answer
1
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
Equilibrium payoff of each player will be
-1.5
1
-1
0
Correct answer
-1
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
If the parties could sign a binding agreement on how much to campaign, what levels would they choose?
a1 = _____________
Correct answer: 0
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
If the parties could sign a binding agreement on how much to campaign, what levels would they choose?
a2 = _____________
Correct answer: 0
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
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
-1.5
1
-1
0
Correct answer
0
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
Now assume that this game is repeated infinitely and the parties cooperate and sign a binding agreement on how much to campaign.
—
Correct answer
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 (a1,a2), the payoff of party i is given by the following function: vi (a1,a2) = ai − 2aj + aiaj − (ai)². Write the normal form representation of this game and answer the given sub-questions.
Now assume that this game is repeated infinitely and the parties cooperate and sign a binding agreement on how much to campaign.
Correct answer
Consider the following game matrix:
| Player 1 \ Player 2 | Slow | Fast |
|---|---|---|
| Slow | 6,6 | 0,2 |
| Fast | 2,0 | 1,1 |
Based on the above data, answer the given subquestions.
Choose the correct alternative(s)
(Slow, Slow) is an NE
(Slow, Fast) is an NE
Both (Slow, Slow) is an NE & (Slow, Fast) is an NE
None
Correct answer
(Slow, Slow) is an NE
Consider the following game matrix:
| Player 1 \ Player 2 | Slow | Fast |
|---|---|---|
| Slow | 6,6 | 0,2 |
| Fast | 2,0 | 1,1 |
Based on the above data, answer the given subquestions.
ESS in this game is (are)
Slow
Fast
Both Slow & Fast
None
Correct answer
Both Slow & Fast
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Suppose one ball is picked from the red majority urn. What is the probability that the ball is blue?
1/3
3/4
1/4
2/3
Correct answer
1/3
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
What is the probability that the urn is majority-red if the first student draws a blue ball?
1/5
4/5
2/3
1/3
Correct answer
1/3
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red).
What is the probability of getting this sequence if the urn is a blue-majority urn?
5/27
4/27
16/125
9/125
Correct answer
4/27
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red).
What is the probability of getting this sequence if the urn is a red-majority urn?
2/27
5/27
5/216
7/216
Correct answer
2/27
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red).
What is the total probability of getting this sequence?
1/25
2/25
1/9
2/9
Correct answer
1/9
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red).
What is the probability of urn being red-majority in this scenario?
2/3
1/25
4/25
1/3
Correct answer
1/3
Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose
Based on the above data, answer the given subquestions.
Ms. A will be paired with
a
b
c
None
Correct answer
None
Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose
Based on the above data, answer the given subquestions.
Ms. B will be paired with
a
b
c
None
Correct answer
a
Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose
Based on the above data, answer the given subquestions.
Ms. C will be paired with
a
b
c
None
Correct answer
b
Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose
Based on the above data, answer the given subquestions.
Ms. D will be paired with
a
b
c
None
Correct answer
None
Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose
Based on the above data, answer the given subquestions.
Ms. E will be paired with
a
b
c
None
Correct answer
c
