Reference · Cheat Sheet 08
Repeated Games & Cooperation
Core idea: Repetition + a valued future + credible retaliation can sustain cooperation that a one-shot game destroys. When the same players interact repeatedly, defection triggers future punishment — and if the future matters enough, cooperation becomes individually rational without communication or altruism.
The four conditions for sustainable cooperation
- Same players must interact repeatedly. The threat of punishment requires a future. One-off interactions have no future to protect, so one-shot logic applies.
Your game: same rival clinic on ads/price month after month — repeated. A walk-in patient who'll never return — one-shot.
- The future must matter enough. Players must be patient (high discount factor) and the horizon must be long or uncertain. A known, fixed last round triggers backward-induction unraveling — cooperation collapses from the final round backward.
Your game: an open-ended vendor relationship casts a long shadow. A 3-month pilot with a known end date has a short one — watch for defection as it closes.
- Defection must be observable and punishable. If the other side can't tell you cheated, the threat has no teeth. Transparent markets (published rates, visible ad spend) help cooperation; opaque pricing hinders it.
- The punishment must be credible. The other player must be willing and able to retaliate. A rival with no capacity to lower prices can't punish your discount — so the threat is empty (see Lesson 07, credibility).
Tit-for-tat — four properties that made it win
Robert Axelrod's tournament winner (The Evolution of Cooperation, 1984)
| Property | What it means | Why it matters |
|---|
| Nice | Never defects first | Earns full cooperation payoff against cooperative strategies; wastes nothing on preemptive hostility |
| Retaliatory | Punishes defection immediately in the next round | Defectors don't get to freeload — the cost of cheating lands fast |
| Forgiving | Returns to cooperation as soon as the other player does | Prevents endless mutual punishment spirals that burn both sides |
| Clear | Pattern is obvious after two rounds | Predictability makes the implicit deal legible — the other player knows what to expect |
The unraveling caveat — finite known horizons
A known final round is cooperation's kryptonite. In the last round, both players defect (no future). Both know this, so the second-to-last round's cooperation is also pointless — both defect there too. Backward induction carries this logic all the way to round 1. The entire cooperative equilibrium unravels.
Fix: keep the horizon open or uncertain, build reputation that extends beyond the relationship, add dimensions (referrals, co-teaching, shared vendors) that extend the shadow even if one channel closes.
Anchor examples for your context
- Price / discount truce (rival clinic): Hold prices cooperatively month-to-month. One defection triggers retaliation; with tit-for-tat, the cooperative path earns more total. Don't announce a clinic closure date — it collapses cooperation immediately.
- Ad spend (Google / Meta vs rival): Competing on the same keywords is a repeated auction game. Overbidding to squeeze the rival triggers counter-escalation — the ad arms race is a PD. Both lose margin to Google. The cooperative path (targeted, non-overlapping campaigns) is individually rational if the relationship is ongoing.
- Referrer relationship (neurosurgeon partner): Each referral is a round. Defection (sending no reciprocal cases, billing disputes, taking credit) collapses the stream. Tit-for-tat: cooperate openly, retaliate once if crossed, forgive when they correct.
- Skull-base course vs competing symposium: Scheduling the same dates, poaching faculty, undercutting fees — all one-shot logic applied to a repeated game. The shadow of the future (annual cycles, shared faculty pool, community reputation) can support a non-overlap truce.
Quick diagnostics
- Is the horizon open or fixed? → Open: shadow present; Fixed: watch for unraveling near the end
- Is defection observable? → Yes: punishment credible; No: shadow weakened
- Are players patient? → Yes: cooperation sustainable at lower gain threshold; No: myopia makes defection tempting
- Is punishment credible? → Yes: tit-for-tat works; No: grim threats are hollow