Game Theory and Cooperation
Strategic interdependence, the Prisoner’s Dilemma, and how cooperation emerges — including when the players are AI.
The previous module treated a single mind deciding under its own limits. But few decisions are made in isolation. The moment two bounded agents must each anticipate the other, a new layer of structure appears — one with its own logic, its own traps, and its own surprising escapes. Game theory is the formal study of that layer, and in the last decade its oldest puzzles have acquired a new kind of player: the machine.
Strategic Interaction: Game Theory Meets AI
When multiple bounded-rational agents interact, something new emerges: strategic interdependence. Your best action depends on what others do, and theirs depends on you. Game theory provides the formal framework, and its central concept — Nash equilibrium, where no player can improve by unilaterally changing strategy — has shaped economics, political science, and evolutionary biology for decades.
The Prisoner’s Dilemma captures the core tension. Two players can cooperate (mutual benefit) or defect (exploit the other). Rational self-interest predicts mutual defection — yet cooperation is clearly better for both. Robert Axelrod’s famous tournaments in the 1980s showed that in iterated games, cooperation can emerge and sustain itself. The winning strategy, Tit-for-Tat, was simple: cooperate first, then mirror whatever the opponent did last. Nice, retaliatory, forgiving, and clear.
The AI era brought dramatic developments. AlphaGo (2016) defeated the world Go champion using moves that human experts found alien but brilliant. AlphaZero (2017) mastered chess, Go, and shogi from scratch through pure self-play — learning entirely by playing millions of games against copies of itself, with no human examples — discovering strategies that centuries of human play had missed. Pluribus (2019) beat professional poker players — the first AI to handle imperfect-information games, where players cannot see each other’s full state, with multiple players. These weren’t just feats of computation; they revealed strategic possibilities that human cognition had never explored. (For the full AI story, see The AI Revolution.)
But when large language models — AI systems like ChatGPT that generate text by predicting the most likely next words, examined in depth in The AI Revolution — entered game-theoretic settings, the results were more nuanced. Research showed GPT-4 cooperates in the Prisoner’s Dilemma about 79% of the time — higher than typical human rates. However, it plays what researchers call an “unforgiving” strategy: it cooperates until the first defection, then permanently retaliates. No forgiveness, no recovery. This makes it “too rational for its own good” — optimizing for not being exploited at the cost of losing all future cooperative gains.
This behavior is prompt-dependent — it shifts with how the question is posed to the model (the prompt). Social Chain-of-Thought prompting — asking the AI to reason about the other player’s perspective before deciding — significantly increases cooperation and forgiveness. The architecture is the same; only the framing changes. This echoes Gigerenzer’s ecological rationality: the “environment” (prompt) determines whether the same system cooperates or defects.
GPT-4 cooperates until betrayed, then permanently defects. Prompt design, not architecture, determines whether AI acts as optimizer or collaborator.
Prisoner's Dilemma Lab
Play iterated Prisoner's Dilemma against different strategies. Try Tit-for-Tat, then the GPT-4 (Unforgiving) strategy. Run the Axelrod-style tournament to see which strategies dominate over hundreds of rounds.
| Opponent | ||
|---|---|---|
| C | D | |
| C | 3,3 | 0,5 |
| D | 5,0 | 1,1 |
Your payoff, Opponent payoff
Round 0/20. Choose Cooperate or Defect:
Game theory reveals that cooperation is not natural — it requires structure. Reputation systems, repeated interaction, and institutional design create the conditions for cooperative equilibria. Structure here is literal: who plays whom matters as much as the payoffs. The same Prisoner’s Dilemma that collapses into mutual defection among strangers can sustain cooperation when players are embedded in a network and imitate successful neighbors.
Cooperation on Networks
Watch cooperation and defection evolve on a network. Agents play Prisoner's Dilemma with their neighbors and imitate successful strategies. Try different network structures — cooperation thrives on clustered lattices but collapses on random networks. Structure determines whether cooperation or defection wins.
Small-world networks let cooperation clusters form, but shortcuts help defectors spread.
Cooperation, then, is an achievement of structure, not a default of nature. The next question follows directly: what happens when the structures that mediate human interaction — the platforms, feeds, and recommendation systems that now sit between us — are redesigned around a different objective entirely? That is the subject of the next module: the contest for attention, and what it does to collective intelligence.