Nash Equilibrium Explained | Why Rational Choices Lead to Bad Outcomes

Описание: Dive deep into Nash Equilibrium—one of game theory's most fundamental concepts. Learn the mathematical foundations, see worked examples with the Prisoner's Dilemma, and understand why individual rationality doesn't always lead to optimal outcomes.

What You'll Learn:
✓ Formal mathematical definition of Nash Equilibrium
✓ The Prisoner's Dilemma with concrete numerical examples
✓ Payoff matrix analysis and dominant strategies
✓ Mixed strategy equilibria and Nash's theorem
✓ Real-world applications in economics, politics, and biology

TIMESTAMPS:
0:00 - Introduction: Rationality vs. Optimal Outcomes
0:15 - Who Was John Nash? Formal Definition
0:35 - Mathematical Definition: Best Response & Utility
0:55 - The Prisoner's Dilemma Setup
1:20 - Numerical Example: Assigning Payoffs
1:40 - Payoff Matrix Construction
2:00 - Strategic Analysis: Prisoner A's Dominant Strategy
2:25 - Prisoner B's Analysis & Finding Equilibrium
2:45 - Suboptimal Results: Individual vs. Collective Rationality
3:05 - Game of Chicken: Multiple Equilibria
3:25 - Analyzing the Chicken Game Equilibria
3:45 - Nash's Theorem: Mixed Strategies
4:15 - Applications: Economics, Politics, Biology

Topics Covered:
• Game Theory Fundamentals
• Strategic Decision Making
• Dominant Strategies
• Payoff Matrices
• Mixed Strategy Equilibria
• Prisoner's Dilemma
• Game of Chicken
• Nash's Existence Theorem