Repeated Games: Playing Again and Again
How playing more than once changes the strategy!
In many real-life situations, people don't just play a game once. They interact with the same people over and over. In Game Theory, we call these Repeated Games.
What Is a Repeated Game?
A game is "repeated" when:
- The same players interact many times
- The rules stay the same each time
- Players can remember what happened in previous rounds
Because the game continues, players can change their behavior based on what others did in the past.
Why Repeating Changes the Game
In a one-time (single-shot) game, a player usually thinks: "What helps me the most right now?"
But in a repeated game, players also think about the future: "If I do this now, how will others treat me next time?"
This long-term view makes cooperation and trust possible.
Example: Two Shop Owners
Imagine two nearby shop owners who sell the same type of bread. Every week, they choose to:
- Cooperate: Keep prices fair so both make a steady profit
- Compete: Lower their price to "steal" the other person's customers
If they only sold bread for one week, lowering the price might seem best. But if they sell bread every week:
- Lowering prices today may start a "price war" tomorrow, where both lose money
- Keeping prices fair builds a partnership that helps both in the long run
Strategies: Having a Plan
In repeated games, a strategy is a rule for how to act based on what happened before. Common strategies include:
- Always Cooperate: Be nice no matter what.
- Always Defect: Look out only for yourself every single time.
- Grim Trigger: Cooperate until the other player cheats once, then never trust them again!
Tit-for-Tat: The Golden Rule of Games
One of the most successful strategies is called Tit-for-Tat. It follows two simple steps:
- Start by cooperating (be nice!)
- In the next round, copy whatever the other player did in the last round
This strategy works because it is:
- Nice: It never starts a fight
- Fair: It responds if the other player is mean, but forgives them if they become nice again
- Clear: Other players can easily understand what you are doing
And when there are many players, all the Tit-for-Tat players cooperate with each other and have many mutual wins.
The Big Idea: Long-Term Thinking
Repeated games show us that sometimes, doing a little worse now (by not "winning" a single round) leads to doing much better later (by building a lasting partnership).
When we value the future, cooperation becomes the smartest way to play.
Where do we see this?
- Friendships: Helping a friend today because you know they'll help you tomorrow
- Business: Companies staying honest to keep their customers coming back
- Environment: Countries working together year after year to protect the planet
Summary
- Repeated games involve the same players and rules over time
- Past actions influence future choices
- Cooperation often emerges because players want to protect their future
- How we play today shapes how others play tomorrow!