Play Again Tomorrow — Game Theory

What changes when the game repeats?

In the cookie-choice lesson, the game happened once. But real life is full of repeat games.

You see the same classmates, teammates, and siblings again tomorrow. That changes everything.

One time only

If the game happens once, grabbing the better deal can feel smartest.

Tomorrow comes

If you play again tomorrow, your choice teaches the other player what to expect.

Many rounds later

A plan that starts kind, answers bad play, and calms down again can do very well over time.

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Meet the four players

Four players enter a tournament. Each plays every other one for 100 rounds:

🕊️ Always Cooperate — always shares
😈 Always Defect — always grabs
🤝 Tit-for-Tat — starts kind, then copies your last move
😤 Grudger — stays kind until you hurt it once, then stays careful forever

The question is not just “Who wins one round?” It is “What pattern grows over many rounds?”

Play it yourself

Pick a strategy and watch two things:

the first few rounds, where the pattern starts
the final score, where that pattern adds up

100 Rounds - Pick Your Plan Your plan will face four different players. Watch the first rounds, then see how the totals grow.

What the first rounds teach

Here’s what happens when Tit-for-Tat plays Always Defect for 100 rounds:

Round 1: TFT cooperates, AD defects -> TFT gets 0, AD gets 5
Rounds 2-100: TFT defects back, AD defects -> both get 1 per round
Final: TFT = 99, AD = 104

And when Tit-for-Tat plays Always Cooperate:

Every round: both cooperate -> both get 3 per round
Final: both get 300

Big idea: in repeat games, a good strategy often starts nice, answers bad behavior quickly, and becomes nice again when the other player improves.

A simple lesson from repeat play

Tit-for-Tat became famous because it is easy to understand:

Nice — it does not start the trouble
Firm — it answers bad play right away
Forgiving — it becomes kind again as soon as you do

Practice

Tit-for-Tat plays 100 rounds against Always Cooperate. What is TFT's score?

Which strategy grabs the most points if it mostly meets very kind players?

Round 1: Tit-for-Tat plays C, Always Defect plays D. TFT gets 0 points. Round 2: TFT copies AD's last move and plays D. Both play D. What does TFT get in round 2?

What is the key lesson from this repeat game?