Why can repeated prisoner’s dilemma games encourage cooperation?
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
In game theory, the prisoner’s dilemma demonstrates that rational, self-interested individuals often fail to cooperate, even when doing so would lead to a better collective outcome.12
While repeating the game might intuitively seem to encourage cooperation through the threat of retaliation, this logic fails if the number of rounds is fixed. Through backward induction, players realize that on the final day, there is no future incentive to cooperate, leading them to defect. This reasoning then cascades backward to the first round, resulting in noncooperation throughout the entire sequence.2
Cooperation becomes a viable strategy primarily when the game is repeated indefinitely or when the players do not know when the sequence will end. In such scenarios, players can adopt "nice" strategies—those that begin with cooperation and reciprocate an opponent's moves. Research, such as the tournament conducted by Robert Axelrod, shows that these strategies, particularly those that are "forgiving" by reverting to cooperation after an opponent does so, outperform purely selfish or non-cooperative approaches.2