Cooperation Over Time

Game Theory · Axiom Academy

Discover how the shadow of the future transforms self-interest into cooperation. In the Prisoner's Dilemma, rational players should defect. But in the real world, we see cooperation everywhere. Why? Click on each outcome to explore the one-shot game. What if the game repeats? Adjust the slider to see how the number of future interactions changes the value of cooperation today. Opponent might cooperate in future rounds. Opponent might punish you in future rounds. Play a repeated Prisoner's Dilemma. Your opponent starts friendly but remembers what you do. Try cooperating, then try defecting, and see what happens! Adjust the "discount factor" to see how much future payoffs matter. When is high, players value the future heavily. When interactions repeat, current actions affect future payoffs. Rational players must consider not just immediate gains, but the entire stream of future consequences. Strategies like Tit-for-Tat use threats of punishment to sustain cooperation. Cooperate as long as your opponent does, but punish defection. These conditional strategies make cooperation self-enforcing. When players are patient enough, many outcomes (including mutual cooperation) can be sustained as equilibria. The folk theorem shows that repetition dramatically expands the set of possible equilibria in games.

This is the written version of the interactive lesson above. See the full Game Theory course.