v Consider the infinitely repeated game of Prisoners’ Dilemma that has the follo

Question

v

Consider the infinitely repeated game of Prisoners’ Dilemma that has the following payoff structure. Each player has a discount rate r. Suppose both players are using the Tit-For-Tat strategy.

Column

Defect

Cooperate

Row

Defect

2, 2

10, 1

Cooperate

1, 10

6, 6

(a) Under what condition does a player have an incentive to deviate once from cooporating and then revert to it? [4 points]

(b) Under what condition does a player have an incentice to deviate from cooporating for ever? [4 points]

(c) Under what condition is it a Nash equilibrium that both players use the Tit-For-Tat strategy? [2 points]

Column

Defect

Cooperate

Row

Defect

2, 2

10, 1

Cooperate

1, 10

6, 6

Explanation / Answer

a) This is prisoner dilemma case both players cheat each others. They deviate and then revert to cooperation again if the case is played for infinite number of times.

b) If the game is played for finite number of times, then player have an incentive to deviate from cooperating for ever.

c) Nash equilibrium refers to the best action of a player provided the action of other player is given. If game is played repeatedly, then each player knows that other will cheat him, thus both player will deviate from the cooperation and adopt the Tit for tat strategy. it would be Nash equilibrium.

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.