Game Theory Week 8 Quiz Answers
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):
- b;
- c;
- y;
- a;
- x;
- z;
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)?
- b;
- y;
- c;
- a;
- z;
- x;
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 pgeq 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):
- When p<1/2p<1/2, it is a Bayesian equilibrium for 1 to enter, 2 to fight when aggressive and not when normal.
- When p=1/2p=1/2, it is a Bayesian equilibrium for 1 to enter, 2 to fight when aggressive and not when normal;
- When p>1/2p>1/2, it is a Bayesian equilibrium for 1 to stay out, 2 to fight when aggressive and not when normal;
- When p=1/2p=1/2, it is a Bayesian equilibrium for 1 to stay out, 2 to fight when aggressive and not when normal;