Game Theory and Strategy Quiz 2: 4 August 2024 (May 2024 term)

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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 red-majority if the first student draws a red ball?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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.

Should the first student guess the urn to be blue majority (in continuation to the previous question)?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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 (Red, Red, Blue).
What is the probability of getting this sequence if the urn is a blue-majority urn?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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 (Red, Red, Blue).
What is the probability of getting this sequence if the urn is a red-majority urn?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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 (Red, Red, Blue).
What is the total probability of getting this sequence?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 3 blue balls and 1 red ball or 3 red balls and 1 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 (Red, Red, Blue).
What is the probability of urn being red-majority in this scenario?

Three sweets are running in an election for the most popular sweet: Gulab jamun (G), Malpua (M), and Balushahi (B). The preference schedule is shown below

No. of votes in thousands

Which candidate wins under the plurality method?

Suppose there are four alternatives, named A, B, C, and D. There are three voters who have the following individual rankings:

$B \succ_1 C \succ_1 D \succ_1 A$

$C \succ_2 D \succ_2 A \succ_2 B$

$D \succ_3 A \succ_3 B \succ_3 C$

Based on the above data, answer the given subquestions.

Using Borda count, the group ranking will be

Suppose there are four alternatives, named A, B, C, and D. There are three voters who have the following individual rankings:

$B \succ_1 C \succ_1 D \succ_1 A$

$C \succ_2 D \succ_2 A \succ_2 B$

$D \succ_3 A \succ_3 B \succ_3 C$

Based on the above data, answer the given subquestions.

Consider two statements about Borda count:
I: Borda Count (ignoring ties) always produces a complete, transitive ranking for a set of alternatives.
II: Outcome in Borda count depends on the presence of alternatives that seem “irrelevant”. Choose the correct alternative about these statements:

Find a stable matching system for the given preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

Men: a, b, c, d.

In a stable matching when men propose to women
Based on the above data, answer the given subquestions.

A will be matched with …………………

Find a stable matching system for the given preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

Men: a, b, c, d.

In a stable matching when men propose to women
Based on the above data, answer the given subquestions.

B will be matched with ………………….

Find a stable matching system for the given preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

Men: a, b, c, d.

In a stable matching when men propose to women
Based on the above data, answer the given subquestions.

C will be matched with ………………….

Find a stable matching system for the given preference structure using the Gale–Shapley algorithm, when the men propose to the women:

Women: A, B, C, D.

Men: a, b, c, d.

In a stable matching when men propose to women
Based on the above data, answer the given subquestions.

D will be matched with …………………..

Consider the following prisoners’ dilemma game and answer the given subquestions.

Unique NE of this game is

Consider the following prisoners’ dilemma game and answer the given subquestions.

Suppose, this game is repeatedly played finite times

Based on the above data, answer the given subquestions.

Find out the value of a = ………….

Based on the above data, answer the given subquestions.

Find out the value of b = ………….
NOTE: Enter your answer in one decimal place.

Based on the above data, answer the given subquestions.

Find out the value of c = ………….
NOTE: Enter your answer in one decimal place.

Based on the above data, answer the given subquestions.

Find out the value of d = ………….

Based on the above data, answer the given subquestions.

Find out the value of p = …………..

Based on the above data, answer the given subquestions.

Find out the value of q = …………
NOTE: Enter your answer in one decimal place.

Based on the above data, answer the given subquestions.

Find out the value of r = …………
NOTE: Enter your answer in one decimal place.

Based on the above data, answer the given subquestions.

Find out the value of t = …………….

Based on the above data, answer the given subquestions.

What is the Bayesian Nash equilibrium in this game?

Consider the following strategic games and answer the given subquestions.

Table 1: Game 1

Table 2: Game 2

NE of the Game 1 is (are)

Consider the following strategic games and answer the given subquestions.

Table 1: Game 1

Table 2: Game 2

NE of the Game 2 is (are)

Consider the following strategic games and answer the given subquestions.

Table 1: Game 1

Table 2: Game 2

Evolutionary Stable Strategy (ESS) in Game 1 is (are)

Consider the following strategic games and answer the given subquestions.

Table 1: Game 1

Table 2: Game 2

Evolutionary Stable Strategy (ESS) in Game 2 is (are)