The prisoner's dilemma represents a situation in which a Nash equilibrium can never be reached.

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While there may be situations in which a Nash equilibrium cannot be reached for the prisoner's dilemma, it is not true in general that such an equilibrium can never be reached. In fact, the classic payoff matrix for the prisoner's dilemma does have a Nash equilibrium (where both prisoners defect), although this outcome is not optimal for either player.

The Prisoner's Dilemma Represents a Situation in Which a Nash