Problem on prisoners dilemma

Prisoners' Dilemma:

In this game there are two players. Let's call them Ace and Betsy. Each player has two choices: Cooperate or Defect. The game will only be played once, and each player must make his or her choice without knowing what the other has decided to do.

The essence of the game is this: if both players Cooperate, they do quite well, and if both Defect, they do quite badly; however, if either Defects while the other Cooperates, the Defector does better than with any other outcome. Thus both players are drawn toward Defecting by its high payoff, but both will lose if both chose to Defect. The situation is illustrated below.

Note that the total payoff is highest if both Ace and Betsy Cooperate (3 + 3 = 6), and lowest if both Defect (1 + 1 = 2). The individual reward to Defect when the other player Cooperates (5), the "temptation to cheat," is higher than the individual reward to Cooperate (3). For example, Ace stands to gain 5 if he Defects and Betsy Cooperates, but if he Defects and Betsy also Defects, he'll only gain 1.

What strategy should these two players choose? Let's take Ace's point of view first. If he knew Betsy would choose to Cooperate, his best choice is to Defect and gain the payoff of 5. On the other hand, if he knew Betsy was going to Defect, his best choice again is to Defect, gaining a payoff of 1 (instead of 0 which he would get if he were to Cooperate).

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