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Game Theory — Prisoner's Dilemma

対象: Universityカテゴリ: Economics

説明

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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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.

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

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

Assets & Dependencies

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

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