In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player iii is described as follows:
There are two "statuses" that player iii might be in during any period: "normal" and "revenge";
In a normal status player iii cooperates;
In a revenge status player iii defects;
From a normal status, player iii switches to the revenge status in the next period only if the other player defects in this period;
From a revenge status player iii 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 ppp that the game continues to the next period and with probability (1−p)(1−p)left parenthesis, 1, −, p, right parenthesis it ends.
Cooperate (C)
Defect (D)
Cooperate (C)
4,4
0,5
Defect (D)
5,0
1,1
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