Game Theory and Strategy Quiz 2: 1 December 2024 (September 2024 term)

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 1 red ball or 4 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 blue 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 4 blue balls and 1 red ball or 4 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 blue-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 4 blue balls and 1 red ball or 4 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 (Blue, Blue, Red).
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 4 blue balls and 1 red ball or 4 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 (Blue, Blue, Red).
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 4 blue balls and 1 red ball or 4 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 (Blue, Blue, Red).
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 4 blue balls and 1 red ball or 4 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 (Blue, Blue, Red).
What is the probability of urn being red-majority in this scenario?

If player 1 chooses 1.5 hour as his action, the best response of player 2 will be

How much negative campaign time each player will choose under a symmetric and unique Nash equilibrium?

Equilibrium payoff of each player will be

Now assume that this game is repeated infinitely. If the parties cooperate and sign a binding agreement on how much to campaign, they choose a1 = a2 = 0.
What will be the payoff of each player in each stage game if they stick to this agreement

Now assume that this game is repeated infinitely. If the parties cooperate and sign a binding agreement on how much to campaign, they choose a1 = a2 = 0.

Now assume that this game is repeated infinitely. If the parties cooperate and sign a binding agreement on how much to campaign, they choose a1 = a2 = 0.

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm, when the women propose:

Based on the above data answer the given subquestions.

Mr. a will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm, when the women propose:

Based on the above data answer the given subquestions.

Mr. b will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm, when the women propose:

Based on the above data answer the given subquestions.

Mr. c will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm, when the women propose:

Based on the above data answer the given subquestions.

Mr. d will be paired with

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of a = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of b = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of c = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of d = ___________.

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of p = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of q = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of r = ___________

(Bayesian Game) Consider a variant of the situation modelled by Battle of Sexes (BoS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/3 player 2 wants to go out with her, and with probability 2/3 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:

With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.

Based on the above data answer the given subquestions.

Find out the value of t = ___________

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 does not depend on the presence of alternatives that seem “irrelevant”.
Choose the correct alternative about these statements: