Overview
This lecture introduces the prisoner's dilemma, a foundational problem in game theory, exploring how cooperation emerges among self-interested individuals and its implications for real-world scenarios.
The Origin and Significance of the Prisoner's Dilemma
- Game theory analyzes strategic decisions where outcomes depend on actions of multiple players.
- The prisoner's dilemma models situations where individuals must choose to cooperate or defect.
- Defecting is the rational individual choice, but mutual defection is worse for both than mutual cooperation.
- The dilemma has real-world implications, from nuclear arms races to everyday social interactions.
Classic Prisoner's Dilemma Setup
- If both players cooperate, each receives three coins.
- If one cooperates and the other defects, the defector gets five coins and the cooperator gets nothing.
- If both defect, each gets one coin.
- Rational players will both defect, leading to a suboptimal outcome.
Repeated Prisoner’s Dilemma and Axelrod’s Tournaments
- Many real-life situations involve repeated interactions, not one-off games.
- Political scientist Robert Axelrod held computer tournaments to test strategies in iterated prisoner's dilemmas.
- Tit for Tat, a simple strategy (cooperate first, then mimic opponent’s previous move), won the tournaments.
- Four key characteristics of successful strategies: being nice, forgiving, retaliatory, and clear.
Strategy Evolution and Environmental Effects
- Successful strategies thrive and multiply, while bad ones go extinct.
- Clusters of cooperative strategies can invade and dominate populations, even among defectors.
- There is no universally best strategy; success depends on the environment and the mix of strategies.
Noise and Error in Iterated Games
- Real-life decisions can be misinterpreted due to noise (errors).
- Noise can trap even good strategies in cycles of retaliation.
- Generous Tit for Tat (retaliates most, but not all, defections) performs better in noisy environments.
Implications and Lessons
- In life, not all interactions are zero sum; mutual cooperation can create more value for everyone.
- Gradual, repeated cooperation (like arms reduction treaties) can help build trust and resolve conflicts.
- Best strategies are nice, forgiving, retaliatory, and clear, but must adapt to the environment.
Key Terms & Definitions
- Game Theory — the mathematical study of strategic decision making.
- Prisoner's Dilemma — a scenario where two players must choose to cooperate or defect, with individual rationality leading to worse joint outcomes.
- Tit for Tat — a strategy that starts with cooperation and then mimics the opponent’s previous move.
- Iterated/Repeated Game — a game played multiple times, allowing strategies to adapt based on past behavior.
- Noise — randomness or errors in interpreting actions.
- Zero Sum Game — a game where one player’s gain is another’s loss.
Action Items / Next Steps
- Review the definitions and characteristics of successful strategies in repeated games.
- Reflect on real-life situations where cooperation or defection affects outcomes.
- (Optional) Explore an introductory probability course to deepen understanding of game theory and strategic decision making.