Repeated games
Repeated games are strategic interactions played many times, allowing reputation and retaliation to shape behaviour.
A game played once and a game played over and over are different worlds. Repetition is what allows trust, reputation, and cooperation to take hold.
Repeated games are strategic interactions that are played many times by the same parties, rather than once. The repetition transforms the strategic logic, because players can condition their behaviour on the past and on expectations of the future, opening the door to cooperation that a single encounter forecloses.
The shadow of the future
The key difference is that, in a repeated game, today's choice has consequences for tomorrow. A player who betrays may gain now but be punished in future rounds, while one who cooperates may build trust that pays off later. This shadow of the future, the prospect of ongoing interaction, gives players a reason to forgo short-term advantage for long-term benefit. The longer and more certain the future, the stronger the incentive to cooperate.
How cooperation becomes rational
In a one-shot prisoner's dilemma, betrayal is rational and cooperation collapses. Repeated, the same game can sustain cooperation, because players can adopt strategies, such as tit for tat, that reward cooperation and punish defection over time. The threat of future retaliation deters betrayal, and the promise of continued cooperation rewards good behaviour, so what was irrational once becomes rational when repeated. This is one of the most important results in game theory: repetition can rescue cooperation that a single encounter would destroy.
Why endings matter
The logic depends on the future being open-ended or at least uncertain. If a repeated game has a known final round, the cooperation can unravel from the end backwards: in the last round there is no future to protect, so betrayal is rational, which makes betrayal rational in the second-to-last round, and so on. This is why indefinite or uncertain horizons, where no one knows when the game ends, sustain cooperation better than fixed, finite ones.
Repeated games explain how trust, reputation, and cooperation arise among self-interested parties without external enforcement, simply through the prospect of continued interaction. They show that the difference between a relationship and a transaction is largely the difference between a game played once and one played again and again.