Game Theory β 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.
Game Theory β 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 β 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 β box it in red |
| 5 | Pareto Optimum | 6s | Show (Cooperate, Cooperate) is better for both β box in green |
| 6 | Nash Formula | 7s | Display Nash Equilibrium formal condition |
| 7 | Conclusion | 5s | Summary of the social dilemma |
Layout
+-----------------------------------------------+
| Game Theory β 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
Audience: UniversityCategory: Economics