Game Theory Week 8 Quiz Answers

In this article i am gone to share Coursera Course Game Theory Week 8 Quiz Answers with you..

Question 1)

Find the strictly dominant strategies (click all that apply: there may be zero, one or more and remember the difference between strictly dominant and strictly dominated):

c;
a;
x;
none
y;
z;
b;

Question 2)

Find the weakly dominated strategies (click all that apply: there may be zero, one or more):

Question 3)

Which strategies survive the process of iterative removal of strictly dominated strategies (click all that apply: there may be zero, one or more)?

Question 4)

Find all strategy profiles that form pure strategy Nash equilibria (click all that apply: there may be zero, one or more):

(a, x);
(c, z).
(b, x);
(b, z);
(a, z);
(b, y);
(a, y);
(c, y);
(c, x);

Question 5)

Which of the following strategies form a mixed strategy Nash equilibrium? (pp corresponds to the probability of 1 playing \color{red}{\verb|b|}b and 1-p1−p to the probability of playing \color{red}{\verb|c|}c; qq corresponds to the probability of 2 playing yy and 1-q1−q to the probability of playing zz).

p=1/4p=1/4, q=1/4q=1/4;
p=2/3p=2/3, q=1/4q=1/4;
p=1/3p=1/3, q=1/3q=1/3;
p=1/3p=1/3, q=1/4q=1/4;

Question 6)

One island is occupied by Army 2, and there is a bridge connecting the island to the mainland through which Army 2 could retreat.

Stage 1: Army 2 could choose to burn the bridge or not in the very beginning.

Stage 2: Army 1 then could choose to attack the island or not.

Stage 3: Army 2 could then choose to fight or retreat if the bridge was not burned, and has to fight if the bridge was burned.

First, consider the blue subgame. What is a subgame perfect equilibrium of the blue subgame?

(Attack, Retreat).
(Attack, Fight).
(Not, Fight).
(Not, Retreat).

Question 7)

One island is occupied by Army 2, and there is a bridge connecting the island to the mainland through which Army 2 could retreat.

Stage 1: Army 2 could choose to burn the bridge or not in the very beginning.

Stage 2: Army 1 then could choose to attack the island or not.

Stage 3: Army 2 could then choose to fight or retreat if the bridge was not burned, and has to fight if the bridge was burned.

What is the outcome of a subgame perfect equilibrium of the whole game?

Bridge is burned, 1 attacks and 2 fights.
Bridge is burned, 1 does not attack.
Bridge is not burned, 1 does not attack.
Bridge is not burned, 1 attacks and 2 retreats.

Question 8)

Consider an infinitely repeated game where the game in each period is depicted in the picture.

There is a probability pp that the game continues next period and a probability (1-p)(1−p) that it ends. What is the threshold p^*p∗ such that when p\geq p^*p≥p∗ ((Play,Share), (Trust)) is sustainable as a subgame perfect equilibrium by a grim trigger strategy, but when p<p^*p<p∗ ((Play,Share), (Trust)) can’t be sustained as a subgame perfect equilibrium?

[Here a trigger strategy is: player 1 playing Not play and player 2 playing Distrust forever after a deviation from ((Play,Share), (Trust)).]

1/3;
2/3;
1/4.
1/2;

Question 9)

There are two players.

The payoffs to player 2 depend on whether 2 is a friendly player (with probability p) or a foe (with probability 1−p).

Player 2 knows if he/she is a friend or a foe, but player 1 doesn’t know.

See the following payoff matrices for details.

When p=1/4p=1/4, which is a pure strategy Bayesian equilibrium:

(1’s strategy; 2’s type – 2’s strategy)

(Left ; Friend – Left, Foe – Right);
(Left ; Friend – Left, Foe – Left);
(Right ; Friend – Right, Foe – Right);
(Right ; Friend – Left, Foe – Right);

Question 10)

Player 1 is a company choosing whether to enter a market or stay out;

If 1 stays out, the payoff to both players is (0, 3).

Player 2 is already in the market and chooses (simultaneously) whether to fight

player 1 if there is entry

The payoffs to player 2 depend on whether 2 is a normal player (with prob 1-p1−p) or an aggressive player (with prob pp).

See the following payoff matrices for details.

Player 2 knows if he/she is normal or aggressive, and player 1 doesn’t know. Which are true (click all that apply, there may be zero, one or more):