Explain why repeated interactions tends to break down the solution of a prisoners' dilemma. Why does the dilemma go away?

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. The dilemma occurs when two prisoners, isolated from each other and unable to communicate, must decide whether to betray the other or remain silent. The payoff matrix for the prisoner's dilemma is as follows: | | Prisoner B Cooperates | Prisoner B Defects | |----------|-----------------------|--------------------| |Prisoner A Cooperates | Both serve 1-year | A serves 3-years, B goes free | |Prisoner A Defects | A goes free, B serves 3-years | Both serve 2-years | The Nash equilibrium in this situation is for both prisoners to defect, as seen by considering what happens if either prisoner were to change their choice unilaterally.

In a repeated interaction scenario (also known as iterated prisoner's dilemma), the same game is played multiple times between the same players. This introduces a new element: the possibility to consider the outcomes of previous rounds and make decisions based on them. In other words, a player can now decide to cooperate or defect based on what happened in previous rounds.

In a one-shot prisoner's dilemma, players have a dominant strategy to defect. However, in a repeated interaction scenario, the optimal strategy may change because players can take into account the other player's behavior and use strategies based on cooperation and reciprocity. An example of a successful iterated prisoner's dilemma strategy is Tit-for-Tat, which starts by cooperating and then mirrors the other player's previous choice in subsequent rounds. Repeated interactions create a situation where the short-term benefits of defection is offset by the potential long-term benefits of cooperation. This is because, by cooperating, players can potentially establish mutual trust and thereby achieve more favorable outcomes over time.

In a repeated interaction scenario, the dilemma created by the prisoner's dilemma situation eventually goes away because players learn from previous rounds and adapt their strategies accordingly. By incorporating the cooperation, retaliation, and forgiveness aspects into their strategies, players are better able to establish trust, reduce the likelihood of defection, and achieve more favorable outcomes. When players are more focused on long-term benefits and recognize the value of cooperation, the dominant strategy of defection in one-shot prisoner's dilemma might no longer be optimal. As a result, the dilemma of whether to cooperate or defect becomes less pronounced and may even disappear entirely if players consistently choose cooperative strategies such as Tit-for-Tat.