# Game Theory Week 5 Quiz Answers

## Game Theory Week 5 Quiz Answers

In this article i am gone to share Coursera Course Game Theory Week 5 Quiz Answers with you..

### Week 5 Quiz Answers

Question 1)
Two players play the following normal form game.

Which is the pure strategy Nash equilibrium of this stage game (if it is played only once)?

• (Left, Left);
• (Left, Middle);
• (Left, Right);
• (Middle, Left);
• (Middle, Middle);
• (Middle, Right);
• (Right, Left);
• (Right, Middle);
• (Right, Right).

Question 2)
Two players play the following normal form game.

Suppose that the game is repeated for two periods. What is the outcome from the subgame perfect Nash equilibrium of the whole game:

• (Left, Left) is played in both periods.
• (Right, Right) is played in both periods.
• (Middle, Middle) is played in the first period, followed by (Left, Left)
• (Middle, Middle) is played in the first period, followed by (Right, Right)

Question 3)
Two players play the following normal form game.

Suppose that 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∗ (Middle, Middle) is sustainable as a subgame perfect equilibrium by grim trigger strategies, but when p < p^*p<p∗ playing Middle in all periods is not a best response? [Here the grim strategy is: play Middle if the play in all previous periods was (Middle, Middle); play Right otherwise.]

• 1/2;
• 1/3;
• 1/4;
• 2/5.

Question 4)
Consider the following game:

Which are the pure strategy Nash equilibria of this stage game? There can be more than one.
• (Left, Right);
• (Left, Left);
• (Left, Middle);
• (Middle, Right);
• (Middle, Left);
• (Right, Right).
• (Right, Middle);
• (Right, Left);
• (Middle, Middle);

Question 5)
Consider the following game:

Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium? (There might be more than one).

• (Left, Left) is played in both periods.
• (Right, Right) is played in both periods.
• (Middle, Middle) is played in the first period, followed by (Right, Right)

Question 6)
Consider the following trust game:

There is a probability pp that the game continues next period and a probability (1-p)(1−p) that it ends. The game is repeated indefinitely. Which statement is true? [Grim trigger in (c) and (d) is player 1 playing Not play and player 2 playing Distrust forever after a deviation from ((Play,Share), (Trust)).]

• There exists a pure strategy Nash equilibrium in the one-shot game with player 2 playing Trust.
• There exists a pure strategy subgame perfect equilibrium with player 2 playing Trust in any period in the finitely repeated game.
• ((Play,Share), (Trust)) is sustainable as a subgame perfect equilibrium by grim trigger in the indefinitely repeated game with a probability of continuation of pgeq5/9p≥5/9.

Question 7)
In an infinitely repeated Prisoner’s Dilemma, a version of what is known as a “tit for tat” strategy of a player ii is described as follows:

• There are two “statuses” that player i might be in during any period: “normal” and “revenge”;
• In a normal status player i cooperates;
• In a revenge status player i defects;
• From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period;
• From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player’s action in this period.

Consider an infinitely repeated game so that with probability pp that the game continues to the next period and with probability (1−p)(1−p) it ends.

True or False:

When player 1 uses the above-described “tit for tat” strategy and starts the first period in a revenge status (thus plays defect for sure), in any infinite payoff maximizing strategy, player 2 plays defect in the first period

• True
• False

Question 8)
In an infinitely repeated Prisoner’s Dilemma, a version of what is known as a “tit for tat” strategy of a player ii is described as follows:
• There are two “statuses” that player i might be in during any period: “normal” and “revenge”;
• In a normal status player i cooperates;
• In a revenge status player i defects;
• From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period;
• From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player’s action in this period.

Consider an infinitely repeated game so that with probability pp that the game continues to the next period and with probability (1−p)(1−p) it ends.

What is the payoff for player 2 from always cooperating when player 1 uses this tit for tat strategy and begins in a normal status? How about always defecting when 1 begins in a normal status?

• 4+4p+4p^2+4p^3+ldots4+4p+4p2+4p3+… ; 5+p+p^2+p^3+ldots5+p+p2+p3+…
• 5+4p+4p^2+4p^3+ldots5+4p+4p2+4p3+… ; 5+p+p^2+p^3+ldots5+p+p2+p3+…
• 5+4p+4p^2+4p^3+ldots5+4p+4p2+4p3+… ; 4+4p+4p^2+4p^3+ldots4+4p+4p2+4p3+…
• 4+4p+4p^2+4p^3+ldots4+4p+4p2+4p3+… ; 5+p+5p^2+p^3+ldots5+p+5p2+p3+…

Question 9)
In an infinitely repeated Prisoner’s Dilemma, a version of what is known as a “tit for tat” strategy of a player ii is described as follows:
• There are two “statuses” that player i might be in during any period: “normal” and “revenge”;
• In a normal status player i cooperates;
• In a revenge status player i defects;
• From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period;
• From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player’s action in this period.

Consider an infinitely repeated game so that with probability pp that the game continues to the next period and with probability (1−p)(1−p) it ends.

What is the threshold p^*p∗ such that when pgeq p^*p≥p∗ always cooperating by player 2 is a best response to player 1 playing tit for tat and starting in a normal status, but when p<p^*p<p∗ always cooperating is not a best response?

• 1/2
• 1/3
• 1/4
• 1/5