Lecture 3: Repeated Games and the Evolution of Cooperation — The Power of Tit-for-Tat

Why Repetition Changes Everything

The core reason betrayal was the dominant strategy in the Prisoner’s Dilemma from Lecture 1 is that it was a one-shot game. When the game repeats, the situation changes fundamentally.

One-Shot Game vs. Repeated Game
Feature	One-Shot Game	Repeated Game
Future Cost	None	Betrayal destroys future cooperation
Reputation	Irrelevant	Being known as a defector causes long-term losses
Optimal Strategy	Defect (dominant strategy)	Conditional cooperation becomes rational
Real Example	One-time deal with a stranger	Business partners, colleagues, neighbors

For cooperation to be possible in a repeated game, players must value future rewards sufficiently. Mathematically, cooperation is an equilibrium when δ (delta) ≥ a critical threshold. The intuition: “Those who think about tomorrow won’t betray today.”

Tit-for-Tat Strategy

Identified as the strongest strategy in Robert Axelrod’s computer tournament (1980).

Round 1: Start with Cooperation

Cooperate unconditionally in the first round. Send a signal of trust.

After: Mirror Your Opponent

If they cooperated, cooperate. If they defected, defect. Respond with exactly one round of delay.

Forgive: Resume Cooperation Immediately

Never retaliate indefinitely. The moment your opponent cooperates again, you cooperate too.

Clarity: Keep the Strategy Simple and Predictable

When opponents understand your strategy, cooperation becomes a stable equilibrium.

Tit-for-Tat's Four Success Factors (Axelrod)
Factor	Explanation	Why the Opposite Fails
Niceness	Never defect first	Defecting first triggers retaliation cycles
Retaliation	Respond immediately to defection	Always cooperating → gets exploited
Forgiveness	Resume cooperation after retaliation	Permanent retaliation → cooperation never recovers
Clarity	Simple and predictable	Complex strategies → misunderstood by opponents

Conditions That Enable Cooperation

Escaping the Prisoner's Dilemma — Conditions for Cooperation
Condition	Mechanism	Real Example
Repeated Interaction	Cost of lost future cooperation > short-term gain from defection	Long-term business partnerships
Reputation System	Public record of defection → loss of future dealings	Marketplace ratings, Airbnb reviews
Small Group Size	Defectors easily identified, social pressure stronger	Village communities, small teams
Shared Identity	Group interest internalized as personal interest	Nations, religions, company culture
Institutional Enforcement	External penalties imposed on defection	Contract law, regulation, standards

The Evolution of Cooperation — Natural Selection and Game Theory

The link between Richard Dawkins’s The Selfish Gene and evolutionary game theory:

Evolutionary Explanations for Altruism
Phenomenon	Evolutionary Game Theory Explanation	Example
Kin Altruism	Shared genes → inclusive fitness	Parental sacrifice, sibling cooperation
Reciprocal Altruism	Repeated game + Tit-for-Tat	Vampire bats sharing blood meals
Group Selection	Cooperative groups outcompete rivals	Cooperative tribes win inter-tribal conflicts
Indirect Reciprocity	Good reputation leads strangers to help	Viral acts of kindness, donation culture

To increase cooperation in an organization: (1) Make the game repeated — emphasize long-term relationships. (2) Introduce reputation systems — make behavior visible and recorded. (3) Keep groups small — teams under 100 people show higher cooperation rates. (4) Define a shared goal clearly — external threats strengthen internal cooperation.

Repeated Games in Practice

Real-World Domains Where Repeated Game Principles Apply
Domain	Repeated Game Structure	Tit-for-Tat in Action
International Trade	Tariff wars vs. trade agreements	WTO: retaliation → rules for resuming negotiations
Workplace Relationships	Colleagues you see every day	Exchanging help, sharing credit
Online Communities	Username = reputation asset	Recognition for contributors, sanctions for bad actors
Family Relationships	Repeated over a lifetime	Reconciliation after conflict, the importance of forgiveness

Key Takeaways

Repeated Game: valuing future rewards → cooperation becomes rational Tit-for-Tat: start cooperating → mirror opponent → forgive immediately — simple but powerful Conditions for Cooperation: repetition + reputation + small groups + shared identity + institutions Evolution: even altruism can be explained evolutionarily through repeated games and kin selection