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Economics & Markets

Game Theory: Infinitely Long

Model #0691Category: Economics & MarketsDepth to apply:
4 min read

On this page

  • Core Idea
  • How to See It
  • How to Use It
  • Founders & Leaders
  • Connected Models
  • One Key Quote
  • Summary & Further Reading

Contents

  1. 1. Core Idea
  2. 2. How to See It
  3. 3. How to Use It
  4. 4. Founders & Leaders
  5. 5. Connected Models
  6. 6. One Key Quote
  7. 7. Summary & Further Reading
·Economics & Markets
Section 1

Core Idea

When a game is repeated indefinitely (no known last period), the set of equilibria expands. In the one-shot prisoner's dilemma, defection dominates. In an infinitely repeated game, cooperation can be sustained if players value the future enough — the "shadow of the future" makes the threat of punishment credible. Folk theorems characterise the payoffs that can be achieved in equilibrium; typically any feasible, individually rational payoff is possible with the right strategies (e.g. tit-for-tat, grim trigger). For founders, the lesson is that long horizons enable cooperation: relationships, reputation, and repeated interaction change the game. Design for repeat play when you want cooperation.
Section 2

How to See It

Partnerships
You're seeing Infinitely Repeated Games when deals and relationships have no clear end. Parties cooperate because defection would trigger retaliation in future rounds. The relationship is the "infinite" horizon.
Reputation
You're seeing it when reputation matters precisely because the game is ongoing. One-shot defection isn't worth it if it destroys future payoffs. Brands and trust are built on this structure.
Strategy
You're seeing it when you ask "will we interact again?" If yes, the effective game is repeated; cooperation and punishment strategies become relevant. If no, one-shot logic applies.
Section 3

How to Use It

When the relationship or market is ongoing, frame it as a repeated game. Cooperate when others do; punish (or exit) when they defect, so that defection isn't profitable. Invest in making the horizon long (contracts, transparency, repeated touchpoints) when you want cooperative outcomes. Short horizons favour defection.
Decision filter
"Is there a next period? If the relationship or game is effectively infinite, cooperation can be an equilibrium — but only if defection is punished. Structure and communication should make that clear."
As a founder
In key partnerships and hires, extend the shadow of the future: multi-year terms, clear consequences for breach, and repeated interaction. That turns one-shot temptation into repeated-game cooperation. When the other side has a short horizon, assume defection risk and protect accordingly.
Section 5

Founders & Leaders

Naval RavikantCo-founder, AngelList; investor and philosopher
Naval often stresses long-term games and "playing the infinite game." That's the repeated-game lens: when the horizon is long, cooperation and fairness can be equilibrium. Founders can adopt it: design relationships and incentives so that the game is repeated and defection is unprofitable.
Section 7

Connected Models

Reinforces
Prisoner's Dilemma
The one-shot prisoner's dilemma has a unique Nash equilibrium (defect, defect). In the infinitely repeated version, (cooperate, cooperate) can be sustained with trigger strategies. The same payoff matrix; the repetition changes the equilibrium set.
Reinforces
Tit-for-tat
Tit-for-tat is a strategy for repeated games: cooperate first, then copy the other's last move. It can sustain cooperation in infinitely (or indefinitely) repeated games when the discount factor is high enough.
Leads-to
Discounting
In repeated games, future payoffs are discounted. The higher the discount factor (the more you value the future), the easier it is to sustain cooperation. Discounting is the bridge between "infinite" and "effective" horizon.
Section 8

One Key Quote

"A finite game is played for the purpose of winning; an infinite game for the purpose of continuing the play. In the infinite game, cooperation and renewal are the point."
— James Carse, Finite and Infinite Games
Section 11

Summary & Further Reading

Infinitely repeated games allow cooperation as equilibrium because the future matters. Use trigger or reciprocal strategies; make defection costly. For founders: extend the shadow of the future to enable trust and cooperation.
01
The Strategy of Conflict — Thomas Schelling (1960)
Book
Credible threats and the value of the future in repeated interaction.
02
The Evolution of Cooperation — Robert Axelrod (1984)
Book
Tit-for-tat and cooperation in repeated games.
03
Game Theory — Drew Fudenberg & Jean Tirole (1991)
Book
Repeated games, folk theorems, and discounting.

Why this matters next

mental modelsIncentives

Game Theory: Infinitely Long applied the Incentives mental model

mental modelsTit-for-tat

Game Theory: Infinitely Long applied the Tit-for-tat mental model

mental modelsCost

Game Theory: Infinitely Long applied the Cost mental model

mental modelsGame Theory

Game Theory: Infinitely Long applied the Game Theory mental model

mental modelsNash Equilibrium

Game Theory: Infinitely Long applied the Nash Equilibrium mental model

mental modelsPrisoner's Dilemma

Game Theory: Infinitely Long applied the Prisoner's Dilemma mental model

Frequently asked questions

What is Game Theory: Infinitely Long?+

Game Theory: Infinitely Long is a mental model used for better thinking and decision-making.

How do you apply Game Theory: Infinitely Long?+

To apply Game Theory: Infinitely Long, identify situations where this framework is relevant, then use it as a lens to evaluate your options and decisions. The model is most useful when combined with other complementary mental models.

What category does Game Theory: Infinitely Long fall under?+

Game Theory: Infinitely Long falls under the Economics & Markets category of mental models. Other models in this category can be found on the Economics & Markets hub page.

Why is Game Theory: Infinitely Long important?+

Game Theory: Infinitely Long is important because it provides a structured way to think about problems that would otherwise be approached with intuition alone. Understanding this model helps you avoid common reasoning errors and make better decisions.

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On this page

  • Core Idea
  • How to See It
  • How to Use It
  • Founders & Leaders
  • Connected Models
  • One Key Quote
  • Summary & Further Reading

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