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Game Theory Week 8 Quiz Answers

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 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):

  • 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;