8. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player i 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 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? a) 4+4p+4p² +4p³ +...; b) 4+4p+4p² + 4p³ + ...; Oc) 5+4p+4p²+4p³ +...; d) 5+ 4p+4p² + 4p³ +...; 5+p+p² + p³ + ... 5+ p + 5p² + p³ + ... 4+4p+4p² + 4p³ +... 5+p+p² + p³ + ...

8. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player i 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 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? a) 4+4p+4p² +4p³ +...; b) 4+4p+4p² + 4p³ + ...; Oc) 5+4p+4p²+4p³ +...; d) 5+ 4p+4p² + 4p³ +...; 5+p+p² + p³ + ... 5+ p + 5p² + p³ + ... 4+4p+4p² + 4p³ +... 5+p+p² + p³ + ...

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

8. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player i 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.
Defect (D)
Cooperate (C)
4,4
0,5
Cooperate (C)
Defect (D)
5,0
1,1
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?
O a) 4 + 4p + 4p² +. 4p³ + ...;
b) 4 + 4p + 4p² + 4p³ +...;
O c) 5+ 4p + 4p² + 4p³ + ...;
O d) 5+ 4p + 4p² + 4p³ + ...;
5+p+p²+p³ +...
5+p+5p²+p³ +...
4 + 4p + 4p² + 4p³ + ...
5+p+p² +p³ +...

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