A game matrix is shown below: Choose the correct statement among the following:

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MAT 3172 Module 1-6 PreTests Answers (Rasmussen College) Section 01

1. A game matrix is shown below: Choose the correct statement among the following:
2. For the game shown below, choose from the options the acceptable integer values of 'x' and 'y' for both players to have strictly dominant strategies.

3. What can be the minimum integer value of 'a' for Player 1 to have a strictly dominant strategy?

4. In the following game, the payoffs are ranks of the outcomes for each player with 1 being the best and 4 being the worst. Identify the correct statement from the options.

5. For the game shown below, choose from the options the acceptable integer values of 'x' and 'y' for both players to have strictly dominant strategies.

6. In the game shown below, the numbers in the cells show payoffs to Players 1 and 2. What is Player 1's dominant strategy?

7. For the game shown below, identify the correct statement from the given options

8. What can be the minimum integer value of 'a' for Player 1 to have a strictly dominant strategy?

9. In the game shown below, the numbers in the cells show payoffs to Players 1 and 2. What is player 1's dominant strategy?

10. For the game shown below, identify the correct statement from the given options

Module 2 Pretest:

1. For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C
2. John randomly picks a number from 1 to 5 (both inclusive) and a letter from A to E (both inclusive). What is the probability that he picks 2 and E?

3. For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C

4. There are 18 boys and 17 girls in a class.One of these students is selected at random to represent the class.

What is the probability that the student selected is a girl?

5. A game matrix is shown below:

6. Bob randomly picks a number from 1 to 6 (both inclusive). What is the probability that he picks a number more than 3?

7. A prisoners' dilemma is a game with all of the following characteristics except one. Choose the characteristic that is not applicable to a prisoners' dilemma game

8. A coin is flipped 3 times. What is the probability of getting two tails and one head?

9. John writes a computer program that produces at random one of these digits:0, 1, 2, 3, 4, 5, 6, 7, 8, 9. What is the probability that the program produces a multiple of 4?

10. Rachel buys a new CD, on which is her favourite track, 8 other tracks she likes and 2 tracks that she does not like. She sets her CD player to play at random.What is the probability that the first track it plays is a track she just likes?

Module 3 Pre Assessment

1. How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?
2. In a game between two teams A and B, John is set to win 200 dollars if A wins, and 100 dollars if B wins. John calculates his expected winning to be 170 dollars. According to John's calculations, what is the probability that B wins (given no probability of a tied/drawn game)?

HINT:  Let the probability that B wins be P, and which means the probabilty that A wins is (1 - P) and then set up the expected value accordingly and solve for P.

3. In a factory, the probability that a manufactured item is defective is 20%. In a lot of 200 items, what is the expected number of defective items?

4. A coin is tossed and if it lands heads you will get 100 dollars. If the coin lands tails you will be paid 50 dollars. What is the expected value of this toss?

5. A fair die is rolled and Rob is offered the dollar value of the number that shows up. What is Rob's expected payoff?

6. There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

7. Out of 10 consecutive integers, two are chosen at random. Find the probability that their sum is odd.

8. What is the probability that after reshuffling, the four S's come consecutively in the word MISSISSIPPI?

9. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, if digits can only be used once?

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Module 4 Pre Assessment

1. Calculate the mixed strategy equilibrium of the game shown below
2. Calculate the mixed strategy equilibrium of the game shown below

3. Calculate the mixed strategy equilibrium of the game shown below

4. Calculate the mixed strategy equilibrium of the game shown below

5. Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned

6. Calculate the pure strategy equilibrium of the game shown below using Minimax method

7. Calculate the pure strategy equilibrium of the game shown below using Minimax method

8. Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned

9. Calculate the pure strategy equilibrium of the game shown below where the payoffs to John have been mentioned

10. Calculate the mixed strategy equilibrium of the game shown below

Module 5 Pre Assessment

1. A game between two players is shown below
2. The payoffs for players 1 and 2 at equilibria (in pure and mixed strategies) are

3. Identify the correct example of a zero sum game from the following

4. A game between two players is shown below

The payoffs for players 1 and 2 at equilibria (in pure strategies) are

5. Identify the zero sum game from the following

6. A game between two players is shown below

The payoffs for players 1 and 2 at equilibria (in pure strategies) are

7. Identify the correct statement from the following

8. Identify the correct statement among the options given below

9. A game between two players is shown below

The payoffs for players 1 and 2 at equilibria (in pure strategies) are

10. In an industry two firms A and B have net annual profits of \$30 million each. If A invests in advertising and B does not, then A's net profit will increase to \$40 million, and B's will decrease to 10 million. Conversely, if B invests in advertising and A does not, then B's net profit will increase to \$40 million and A's will decrease to \$ 10 million. However, if both invest in advertising neither A nor B will have any incremental advantage and both the firms will have profits of \$20 million. If neither A nor B advertises both continue to have profits of \$30 million each. Both A and B decide simultaneously from choices: 'Advertise' and 'Don't Advertise'. What is the Nash Equilibrium of this game?

11. Identify the zero sum game from the following

Module 6 Pre assessment

1. Identify the SPE of the game
2. Identify the SPE of the game

3. At equilibrium, choose the correct option from the following

4. Two Firms A and B are playing the following game where A is deciding whether to enter B’s market.

The numbers are the payoffs for Firm A and B respectively.

If B accommodates, Firm A should choose

5. Two Firms A and B are playing the following game where A is deciding whether to enter B’s market.

The numbers are the payoffs for Firm A and B respectively.

If A chooses to Enter, Firm B should choose

6. Two Firms A and B are playing the following game as shown

The numbers are the payoffs for Firm A and B respectively.

If A chooses L, B should choose

7. Two Firms A and B are playing the following game as shown

The numbers are the payoffs for Firm A and B respectively.

Identify the payoffs to A and B at SPE

8. Two players Bob and Alice are playing the following game

The numbers in the cells are the respective payoffs to the players as per convention

If Bob chooses 'Fight' with probability 'p' and Alice chooses 'Fight' with probability 'q', for x=y=10, the mixed strategy equilibrium is

9. Two Firms A and B are playing the following game where A is deciding whether to enter B's market.

The numbers are the payoffs for Firm A and B respectively.

If B chooses to Fight, Firm A should choose

10. A sequential game is shown below:

At equilibrium, choose the correct option from the following