ms4023_2025T3_Q1_NA.pdf
Game Theory and Strategy · Quiz 1 · Sep 2025
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Question 93 MCQ · 2.0 marks
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A published solution is not available for this question yet.
Question 94 MCQ · 2.0 marks
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Choose the incorrect statement
This game is a symmetric game
This game has a symmetric Nash equilibrium
Under the Nash equilibrium each player chooses P=15
This game has unique Nash equilibrium
A published solution is not available for this question yet.
Question 95 MCQ · 2.0 marks
**(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.
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Choose the correct alternative
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
Both 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
None
A published solution is not available for this question yet.
Question 96 MCQ · 2.0 marks
**(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.
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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
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
Both 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
None
A published solution is not available for this question yet.
Question 97 MCQ · 2.0 marks
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.
Which player does not have strictly dominated strategy?
Player 1
Player 2
None
A published solution is not available for this question yet.
Question 98 MCQ · 2.0 marks
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.
Which strategies survive Iterated Elimination of Strictly Dominated Strategy?
(0, 0)
(1, 1)
(2, 2)
None
A published solution is not available for this question yet.
Question 99 MCQ · 2.0 marks
Consider the following normal form game and answer the given
This game has
A unique Nash equilibrium in pure strategy
A unique Nash equilibrium in mixed strategy
Both are true
None is true
A published solution is not available for this question yet.
Question 100 NAT · 3.0 marks
Consider the following normal form game and answer the given
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A published solution is not available for this question yet.
Question 101 MCQ · 1.0 marks
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:
This is a game of
Perfect information
Imperfect information
None
Can’t be determined
A published solution is not available for this question yet.
Question 102 MCQ · 1.0 marks
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:
How many terminal nodes does this game have?
3
2
4
5
A published solution is not available for this question yet.
Question 103 MCQ · 1.0 marks
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:
How many information sets does this game have?
2
3
4
1
A published solution is not available for this question yet.
Question 104 MCQ · 1.0 marks
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:
How many pure strategies does player 1 have?
1
2
3
4
A published solution is not available for this question yet.
Question 105 MCQ · 1.0 marks
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:
How many pure strategies does player 2 have?
1
2
3
4
A published solution is not available for this question yet.
Question 106 MCQ · 1.0 marks
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:
How many pure strategy Nash equilibria does this game have?
1
2
3
4
A published solution is not available for this question yet.