Game Theory — Prisoner's Dilemma

Description

Introduces the Prisoner's Dilemma, a foundational concept in game theory. Shows a 2x2 payoff matrix, animates two prisoners making independent decisions, explains why (Defect, Defect) is the Nash Equilibrium even though mutual cooperation is Pareto superior. Highlights dominant strategies and the Nash Equilibrium condition.

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Phases

#	Phase Name	Duration	Description
1	Setup Story	6s	Two prisoners are arrested — cannot communicate
2	Payoff Matrix	10s	Build the 2x2 matrix cell by cell with payoffs
3	Dominant Strategy	8s	Highlight that Defect dominates Cooperate for each player
4	Nash Equilibrium	8s	Show (Defect, Defect) is Nash Equilibrium — box it in red
5	Pareto Optimum	6s	Show (Cooperate, Cooperate) is better for both — box in green
6	Nash Formula	7s	Display Nash Equilibrium formal condition
7	Conclusion	5s	Summary of the social dilemma

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Layout

+-----------------------------------------------+
|        Game Theory — Prisoner's Dilemma        |
|                                                |
|   Prisoner B:   Cooperate    Defect            |
|                +----------+----------+         |
| Prisoner A:    |          |          |         |
|  Cooperate     |  -1, -1  |  -10, 0  |         |
|                +----------+----------+         |
|  Defect        |  0, -10  |  -5, -5  |         |
|                +----------+----------+         |
|                                                |
|  Nash Eq: (Defect, Defect) = (-5, -5)         |
|  But (Cooperate, Cooperate) = (-1, -1)         |
|  is better for both!                           |
+-----------------------------------------------+

Area Descriptions

• Top: Title
• Center: 2x2 payoff matrix built incrementally
• Bottom-left: Dominant strategy explanation
• Bottom-right: Nash Equilibrium formula

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• Matrix cells highlighted in sequence
• Nash equilibrium cell boxed in red
• Pareto optimal cell boxed in green
• Prisoner icons represented as simple stick figures or labeled circles
• Background: dark navy #1a1a2e