Mastering the Prisoner's Dilemma for AP Micro Exam Success

📚 Quick Study Guide

• ⚖️ The Prisoner's Dilemma is a standard example of a game analyzed in game theory that shows why two completely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.
• 🧑‍🤝‍🧑 In the classic scenario, two suspects are arrested for a crime. They are held in separate cells and cannot communicate.
• 🤝 The authorities offer each prisoner a deal: betray the other (defect) or cooperate (remain silent).
• 📜 The possible outcomes are typically presented in a payoff matrix:

  	Prisoner B Stays Silent	Prisoner B Betrays
  Prisoner A Stays Silent	Both serve 1 year	A serves 10 years, B is free
  Prisoner A Betrays	A is free, B serves 10 years	Both serve 5 years

• 🎯 The dominant strategy for both prisoners is to betray, even though both would be better off if they both remained silent. This leads to a Nash equilibrium where both are worse off.
• 📈 The Prisoner's Dilemma illustrates concepts like cooperation, competition, dominant strategies, and Nash equilibrium.
• 💸 Applications extend beyond criminal scenarios and include economics, business, and even environmental issues.

Practice Quiz

1. What is the core problem illustrated by the Prisoner's Dilemma?
   1. A) Individuals always act in their collective best interest.
   2. B) Rational individuals may not cooperate, even when it's beneficial.
   3. C) Cooperation is always the best strategy.
   4. D) Authorities always offer fair deals.
2. In the Prisoner's Dilemma, what is a 'dominant strategy'?
   1. A) A strategy that leads to the best outcome for both players, regardless of the other's choice.
   2. B) A strategy that is always the best choice for a player, regardless of the other's choice.
   3. C) A strategy that relies on the other player's cooperation.
   4. D) A strategy that guarantees the player will go free.
3. What outcome represents the Nash Equilibrium in the classic Prisoner's Dilemma?
   1. A) Both prisoners remain silent.
   2. B) One prisoner betrays, and the other remains silent.
   3. C) Both prisoners betray each other.
   4. D) One prisoner confesses, and the other gets a reduced sentence.
4. Which of the following is NOT a common application of the Prisoner's Dilemma?
   1. A) Economics
   2. B) Business
   3. C) Environmental issues
   4. D) Celestial mechanics
5. What is the likely outcome if both prisoners choose to betray each other?
   1. A) Both go free.
   2. B) One goes free, the other serves a long sentence.
   3. C) Both serve a moderate sentence.
   4. D) Both serve a minimal sentence.
6. If Prisoner A stays silent and Prisoner B betrays, what is the outcome?
   1. A) Prisoner A goes free, Prisoner B serves a long sentence.
   2. B) Prisoner B goes free, Prisoner A serves a long sentence.
   3. C) Both serve a moderate sentence.
   4. D) Both serve a minimal sentence.
7. What does the Prisoner's Dilemma demonstrate about cooperation?
   1. A) Cooperation is always the optimal strategy.
   2. B) Cooperation is impossible in competitive situations.
   3. C) Cooperation can be difficult to achieve even when it's mutually beneficial.
   4. D) Cooperation is only possible with external enforcement.