Prisoner's Dilemma Overview

Overview

This lecture introduces the prisoner's dilemma, a classic scenario in game theory, and explains its possible outcomes and the reasoning behind rational choices. The example uses two characters, Rabbit and Red Dog, to illustrate how the dilemma works and why it can be difficult to understand at first.

Prisoner's Dilemma Setup

• The prisoner's dilemma involves two individuals, Rabbit and Red Dog, who have been caught for a crime.
• They are complete strangers, have no relationship, and will not interact again. Each only cares about their own outcome.
• There are no outside consequences—no threats, rewards, or future interactions—just the prison sentences they might receive.
• Each must independently decide whether to stay silent or betray ("rat out") the other.
• Their choices are shown in a decision matrix, where Rabbit’s choices are the rows and Red Dog’s choices are the columns.

Sample Decision Matrix:

(Note: The years are just an example; the actual numbers can vary, but the relationships between outcomes stay the same.)

Possible Outcomes

• Both stay silent:
  • Each gets their second-best outcome (e.g., 2 years in prison).
• Both betray (rat):
  • Each gets their second-worst outcome (e.g., 4 years in prison).
• Rabbit stays silent, Red Dog betrays:
  • Rabbit gets the "sucker's payoff" (worst outcome, e.g., 5 years), Red Dog gets their best (e.g., 0 years).
• Rabbit betrays, Red Dog stays silent:
  • Rabbit gets their best outcome (e.g., 0 years), Red Dog gets the "sucker's payoff" (worst, e.g., 5 years).

Sample Scenarios:

• If you (Rabbit) stay silent and Red Dog rats, you get the worst deal (5 years), while Red Dog goes free.
• If you both rat, you both get a bad deal (4 years), but not as bad as being the only one who stays silent.

Rational Decision-Making

• Each player considers the possible actions of the other:
  • If the other stays silent, betraying gives you the best outcome (go free).
  • If the other betrays, betraying means you avoid the worst outcome (you get 4 years instead of 5).
• No matter what the other person does, betraying is always the better choice for you. This is called a "strictly dominant strategy."
• The trap: Because both reason this way, both end up betraying, and both get a worse outcome (4 years) than if they had both stayed silent (2 years).

Step-by-Step Example:

1. Imagine you are Rabbit.
2. If you think Red Dog will stay silent, you can get 0 years by betraying (instead of 2 years by staying silent).
3. If you think Red Dog will betray, you get 4 years by betraying (instead of 5 years by staying silent).
4. In both cases, betraying is better for you.
5. Red Dog reasons the same way, so both betray.

Changing the Outcome

• The only way to escape the prisoner's dilemma is to change the payoff structure so that cooperation (both staying silent) becomes the rational choice.
• In real life, factors like personal relationships, repeated interactions, or threats can change the incentives.
  • For example, if Rabbit and Red Dog were friends or knew they would meet again, they might be more likely to cooperate.
  • If there were extra consequences for betraying (like "snitches get stitches"), the payoffs would change, and cooperation might become more attractive.

Sample Real-World Changes:

• If betraying leads to social punishment or danger, staying silent might become the better choice.
• If the game is repeated (they might be caught again in the future), they might cooperate to build trust.

Key Terms & Definitions

• Prisoner's Dilemma: A situation where two people are tempted to betray each other, even though both would be better off cooperating.
• Decision matrix: A table that shows all possible choices and outcomes for each player.
• Sucker's payoff: The worst outcome for a player who cooperates while the other betrays (e.g., 5 years in prison).
• Strictly dominant strategy: A strategy that is always better for a player, no matter what the other person does (in this case, betraying).

Action Items / Next Steps

• Review the written lectures for more detailed explanations and additional examples.
• Practice drawing and filling out decision matrices to better understand the reasoning.
• Think about how changing the payoffs (adding relationships, repeated games, or consequences) would affect the choices.
• Prepare for assignments by making sure you understand why rational players end up betraying, and how the dilemma can be changed in real life.