Question 102 NAT · 3.0 marks
What is the minimum number of steps required to produce the integer **750**?
A published solution is not available for this question yet.
ms4023_2024T3_Q1_NA.pdf
Game Theory and Strategy · Quiz 1 · Sep 2024
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Question 104 MCQ · 1.0 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 105 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 106 MCQ · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
Choose the correct statement
- There is a unique Nash equilibrium in pure strategy
- There are finitely many Nash equilibria in this game in pure strategy
- There is no Nash equilibrium in this game in pure strategy
- None
A published solution is not available for this question yet.
Question 107 MCQ · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
Choose the correct statement
- There is a unique Nash equilibrium in this game
- There are finitely many Nash equilibria in this game
- There is no Nash equilibrium in this game
- None
A published solution is not available for this question yet.
Question 108 NAT · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
If the randomization probability of a police officer for patrolling the streets is p/13, then p
=__________
A published solution is not available for this question yet.
Question 109 NAT · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
If the randomization probability of a police officer for patrolling the park is q/13, then q = ________
A published solution is not available for this question yet.
Question 110 NAT · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
If the randomization probability of the drug dealer choosing street is r/13, then r =_______________
A published solution is not available for this question yet.
Question 111 NAT · 1.0 marks
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to
disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on
a street corner or in the park. Each day, he decides where to set up shop, knowing that word
about his location will travel among users. Because a good snitch is lacking, word does not travel
to the police. The police officer on the beat then needs to decide whether she will patrol the park
or the street corner, while not knowing where the drug dealer is hanging out that day.
The decision of the officer and the dealer determine the extent of drug trades that day. Let
suppose the total number of potential trades in the market is 100. A dealer's payoff is determined
by the number of trades he consummates, while the officer’s payoff is based on the number of
trades she disrupts. The table below illustrates the payoffs for both parties according to their
respective strategies in the game.
[[IMAGE:71f008a1263412ac_3_0]]
Based on the above data, answer the given subquestions.
If the randomization probability of the drug dealer choosing park is s/13, then s = _____________
A published solution is not available for this question yet.
Question 112 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 113 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 114 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 115 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 116 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 117 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.
Question 118 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:
Which one of the Nash equilibria is also a subgame perfect equilibrium?
- (AE, D)
- (AF, D)
- (BE, C)
- (BF, C)
A published solution is not available for this question yet.
Question 119 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:
No. of sub games this game has
- 1
- 2
- 3
- 4
A published solution is not available for this question yet.
Question 120 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.
[[IMAGE:71f008a1263412ac_8_1]]
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
- In Nash equilibrium two people take each route and 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 121 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.
[[IMAGE:71f008a1263412ac_8_1]]
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. Find the Nash
equilibrium in this new situation and answer the questions.
Choose the correct alternative
- In any Nash equilibrium, one person takes A–X–B, two people take A–X–Y–B, and one person takes A–Y–B
- In this equilibrium profile, each person’s travel time is 36 minutes
- In any Nash equilibrium, one person takes A–X–B, two people take A–X–Y–B, and one person takes A–Y–B and In this equilibrium profile, each person’s travel time is 36 minutes
- None
A published solution is not available for this question yet.
Question 122 MCQ · 2.0 marks
[[IMAGE:71f008a1263412ac_9_2]]
Based on the above data, answer the given subquestions.
[[IMAGE:71f008a1263412ac_9_3]]
- [[IMAGE:71f008a1263412ac_9_4]]
- [[IMAGE:71f008a1263412ac_9_5]]
- [[IMAGE:71f008a1263412ac_9_6]]
- [[IMAGE:71f008a1263412ac_9_7]]
A published solution is not available for this question yet.
Question 123 MCQ · 2.0 marks
[[IMAGE:71f008a1263412ac_9_2]]
Based on the above data, answer the given subquestions.
Choose the correct alternative
- [[IMAGE:71f008a1263412ac_10_8]]
- [[IMAGE:71f008a1263412ac_10_9]]
- [[IMAGE:71f008a1263412ac_10_10]]
- [[IMAGE:71f008a1263412ac_10_11]] **Market Research** **Section Id :** 64065369316 **Section Number :** 7 **Section type :** Online **Mandatory or Optional :** Mandatory **Number of Questions :** 30 **Number of Questions to be attempted :** 30 **Section Marks :** 50 **Display Number Panel :** Yes **Section Negative Marks :** 0 **Group All Questions :** No **Enable Mark as Answered Mark for Review and** No **Clear Response :** **Section Maximum Duration :** 0 **Section Minimum Duration :** 0 **Section Time In :** Minutes **Maximum Instruction Time :** 0
A published solution is not available for this question yet.