9. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 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 p that the game continues to the next period and with probability (1-p) it ends. Cooperate (C) Defect (D) Cooperate (C) 4,4 5,0 Defect (D) 0,5 1,1 What is the threshold p* such that when 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* always cooperating is not a best response? ◇ a) 1/2 ○ b) 1/3 ○ c) 1/4 ○ d) 1/5
9. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 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 p that the game continues to the next period and with probability (1-p) it ends. Cooperate (C) Defect (D) Cooperate (C) 4,4 5,0 Defect (D) 0,5 1,1 What is the threshold p* such that when 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* always cooperating is not a best response? ◇ a) 1/2 ○ b) 1/3 ○ c) 1/4 ○ d) 1/5
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:9.
In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 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 p that the game continues to the next period and with probability (1-p) it ends.
Cooperate (C)
Defect (D)
Cooperate (C)
4,4
5,0
Defect (D)
0,5
1,1
What is the threshold p* such that when 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* always cooperating is not a best response?
◇ a) 1/2
○ b) 1/3
○ c) 1/4
○ d) 1/5
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