Ch 1: Prisoner's Dilemma & Payoff Matrix
1. The Conflict Between Individual and Group
One of the most famous and important cases in game theory, the Prisoner’s Dilemma, poses a profound question:
“Why do we end up betraying each other even when there’s a better outcome for everyone?”
The Scenario
Two suspects are interrogated in separate rooms. The prosecutor offers the following conditions:
- If both stay silent (cooperate), they each get 1 year in prison due to insufficient evidence.
- If only one confesses (betrays), that person is released immediately, and the one who stayed silent gets 5 years.
- If both confess (betray), they each get 3 years.
2. The Payoff Matrix
The set of numbers organizing this situation is called the Payoff Matrix. (Higher numbers represent better outcomes, i.e., less prison time.)
| Me \ Opponent | Cooperate (Silent) | Betray (Confess) |
|---|---|---|
| Cooperate (Silent) | 3, 3 | 0, 5 |
| Betray (Confess) | 5, 0 | 1, 1 |
Analysis: Why is betrayal ‘rational’?
Regardless of what the other person does, it’s always more advantageous for me to betray.
- If they cooperate: Betrayal (5) is better than cooperation (3).
- If they betray: Betrayal (1) is better than cooperation (0).
In the end, two rational prisoners will both choose to betray, resulting in a worse outcome (3 years) than if they had both cooperated (1 year). This is the tragedy of non-cooperative games.
Today’s Assignment Find a situation in daily life that resembles the ‘Prisoner’s Dilemma’ (e.g., climate change response, shared office fridge). What mechanism would be needed to break this dilemma?
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