Overview
This lecture explains the Prisoner's Dilemma, a fundamental problem in game theory, illustrating its significance in international conflict, biology, and the emergence of cooperation.
The Origin of the Prisoner's Dilemma
- The US detected Soviet nuclear tests in 1949, escalating Cold War tensions.
- The RAND Corporation used game theory to analyze nuclear strategy.
- Mathematicians at RAND invented the Prisoner's Dilemma in 1950.
Prisoner's Dilemma Explained
- Two players choose to cooperate or defect for rewards.
- Mutual cooperation yields moderate rewards; mutual defection yields low rewards.
- Each player's rational move is to defect, leading to suboptimal outcomes for both.
Real-World Example: US-Soviet Arms Race
- Both countries developed massive nuclear arsenals, harming both sides.
- Mutual cooperation would have been better but was not achieved due to mistrust.
Iterated Prisoner's Dilemma and Axelrod's Tournaments
- Real-life dilemmas often repeat, changing strategic considerations.
- Robert Axelrod organized computer tournaments to find optimal strategies.
- The simplest and most effective strategy was Tit for Tat: cooperate first, then copy the opponent's previous move.
Key Qualities of Successful Strategies
- Top strategies were nice (never defect first), forgiving (let go of past defections), retaliatory (respond to defection), and clear (predictable).
- Too-forgiving or too-nasty strategies performed poorly.
- No single best strategy exists; effectiveness depends on the population.
Evolution and Emergence of Cooperation
- In simulated evolution, nice strategies like Tit for Tat flourish over generations.
- Clusters of cooperative players can spread cooperation in otherwise selfish environments.
- Cooperation can emerge even among self-interested agents without trust.
The Impact of Noise and Error
- Random errors (misinterpreted moves) can trigger cycles of retaliation.
- Generous Tit for Tat (retaliate most but not all the time) works better in noisy environments.
- Long-term payoff comes from finding mutual benefit, not just beating the opponent.
Applications and Broader Lessons
- The principles from Axelrod's tournaments apply to biology, international relations, and everyday life.
- US and Soviet gradual disarmament resembled iterated cooperation.
- Most of life’s dilemmas are not zero-sum; cooperation often produces the best outcomes.
Key Terms & Definitions
- Prisoner's Dilemma — A game where two players choose to cooperate or defect, with rewards structured so mutual cooperation is best but each has an incentive to defect.
- Tit for Tat — A strategy that starts with cooperation and then mimics the opponent’s previous move.
- Iterated Game — A game repeated multiple times, allowing for strategies that depend on previous outcomes.
- Zero-sum Game — A situation where one player’s gain is exactly another’s loss.
Action Items / Next Steps
- Reflect on how cooperative strategies can benefit group outcomes in repeated interactions.
- If assigned, read further on Axelrod’s research and its applications in biology or politics.