Play the same cooperate-or-betray dilemma two ways: once as a single, one-shot encounter, and once as a repeated game where there's always a chance of one more round. Watch how your strategy — and your opponent's — changes.
Choose a game mode to play against a Tit for Tat opponent
Chance of another round (for Repeated Game): 80%
When there's a good chance of "another round," betraying today can cost you tomorrow. This looming possibility of future interaction is called the shadow of the future — and it's often what makes cooperation worthwhile.
This lesson explores one of the most important ideas in game theory: the difference between a one-shot game and a repeated game. In a one-shot game, you play a dilemma exactly once and then it's over forever — there's no way for your opponent to punish you for betraying them, and no way for you to build trust for the future. Because of this, the "rational" choice in a one-shot Prisoner's Dilemma-style game is usually to betray, since you get a better payoff no matter what your opponent does, and there's no tomorrow to worry about.
But real life rarely works this way. Most relationships — friendships, business partnerships, neighborhood interactions — are repeated games where you expect to interact with the same people again and again. This changes everything. If there's a high chance you'll meet this person again, betraying them today might earn you a quick win, but it risks retaliation and lost cooperation in every future round. This concept is called the shadow of the future: the more likely future interactions are, the more that possibility "casts a shadow" back onto today's decisions, encouraging cooperation.
Game theorists model this using a "continuation probability" — the chance that another round will happen. When that probability is low, players act more like they're in a one-shot game, since the future barely matters. When it's high, players have strong incentives to cooperate, because the potential future losses from retaliation dwarf the one-time gain from betrayal. This is exactly why the interactive game above lets you adjust the "chance of another round" slider — a higher setting means cooperation becomes the smarter long-term strategy, while a low setting starts to resemble the one-shot game where betrayal is more tempting.
This idea helps explain a huge range of human behavior: why people are politer to regular customers than strangers passing through, why long-term business partners treat each other more fairly than one-time deals, and why societies build institutions like reputations, contracts, and laws to extend the "shadow of the future" even into interactions that might otherwise feel like one-shot games.
With a partner, play the cooperate-or-betray game above two different ways. First, agree you'll only play once — see what everyone chooses. Then play again, but this time roll a die after each round: if it lands on 1-5, you play another round, and only a 6 ends the game (an 83% continuation chance). Compare how often people chose to betray in the one-shot version versus the repeated version, and discuss why.
What does "shadow of the future" mean?
The shadow of the future describes how the possibility of interacting again in the future changes how people behave today, making cooperation more likely when future rounds are probable.
Why is cheating more tempting in a one-shot game?
In a one-shot game there's no tomorrow, so there's no way for the other player to punish betrayal later, removing the main incentive to cooperate.
What happens as the chance of another round increases?
As the probability of future rounds rises, players have more to lose by betraying each other, so cooperation becomes a more rational and common strategy.
Where is the shadow of the future important in real life?
It matters in long-term business relationships, friendships, international relations, and any situation where people expect to interact again, versus one-time interactions like a single purchase from a stranger.