Four ideas, before anything else#

• one-shot game
• the folk theorem
• shadow of the future
• tit-for-tat

Get these four straight now — the tournament next uses all of them.

One-shot game#

If you were only ever going to see this person once, there’d be no reason to be generous, forgiving, or even honest about small things — nothing you do today can be answered tomorrow, because there is no tomorrow.

A game played exactly once, with no future round to reward or punish what happened, is a one-shot game — and in a one-shot prisoner’s dilemma, selfishness is the only equilibrium.

Shadow of the future#

The moment you expect to see the same person again — same friend group, same apartment, same relationship — every choice today casts a shadow forward. Being unkind now can be answered later; being generous now can be banked on later, too.

Economists call how much weight today’s choice gives to future rounds the shadow of the future — and it’s the single variable that decides whether cooperation can survive.

The folk theorem#

Here’s the striking part: once the shadow of the future is long enough, it’s not just cooperation that becomes possible — almost any pattern of behavior both sides can live with becomes a sustainable equilibrium, provided each side can credibly punish the other for breaking it.

That result is the folk theorem — repetition doesn’t just allow cooperation, it explodes the number of equilibria the game can settle into.

Tit-for-tat#

Faced with that explosion of possible equilibria, one simple rule keeps winning in practice: start by cooperating, then do back to your partner exactly what they just did to you. Nothing more elaborate than that.

That rule is tit-for-tat, and its success isn’t about being clever — it’s about being instantly readable, quick to forgive, and impossible to exploit for long.

One bad month, two possible worlds#

Nothing about either person changed between the columns. Only how long they expect to keep playing did.

Running tit-for-tat on the bad month#

One missed month costs exactly one round of retaliation, then the relationship self-corrects — if both sides are reading tit-for-tat and not something harsher.

What if a mistake gets misread?#

Swap Friend B’s rule from tit-for-tat to grim trigger: defect forever after the first defection, no matter what happens next.

Same bad month. A stricter rule turns one missed payment into the end of the arrangement — the strategy chosen, not the mistake itself, decided how much a single bad month was allowed to cost.

Back to week 9#

A negotiated split (week 9) isn’t self-enforcing on its own — nothing stops either side from quietly grabbing more the moment they think it’s the last round. What actually holds a split together, month after month, is exactly this week’s shadow of the future: the expectation of enough future rounds that breaking the deal now costs more than it gains.

What today doesn’t settle#

The folk theorem proves cooperation can be an equilibrium once the shadow of the future is long enough — but so can almost anything else two sides can credibly threaten each other into. The model has no way to say which equilibrium two real people actually land in, and no built-in account of how much forgiveness a strategy should carry before one bad month becomes a permanent grudge.

That’s week 7’s gap again, one level up: week 7 couldn’t say who breaks a standoff between two people on one night; this week, the same missing ingredient decides which of many possible relationships two people spend years living inside.

Week 12 is where this, and every prior week’s gap, come back at once.