🎲 Introduction to Game Theory
Based on Jennifer Firkins Nordstrom's textbook, licensed CC BY-SA 4.0.
Same format as the paper pages: runnable Python, diagrams, plain English. If you're reading the Hedges 2018 page and want to know what Nash equilibrium actually means, start here.
| Section | One sentence | |
|---|---|---|
| Ch 1. What is Game Theory? | ||
| Players and Strategies | A game is players, strategies, and payoffs — everything else is commentary | 🎲 |
| Game Matrices | Every simultaneous two-player game fits in a payoff matrix | 🎲 |
| Ch 2. Two-Person Zero-Sum Games | ||
| Zero-Sum Games | Your gain is my loss — the payoffs always sum to zero | 🎲 |
| Dominated Strategies | If strategy A is always worse than B, delete it — rational players never use it | 🎲 |
| Probability and Expected Value | Mixing strategies randomly lets you do better than any fixed choice | 🎲 |
| Equilibrium Points | A pair of strategies where neither player wants to switch — Nash equilibrium | 🎲 |
| Zero-Sum Summary | Minimax, maximin, and when they meet: the saddle point | 🎲 |
| Ch 3. Repeated Two-Person Zero-Sum Games | ||
| Repeated Games | Play the same game many times and the best strategy is a probability distribution | 🎲 |
| Mixed Strategies: Graphical | Plot expected payoffs against mixing probability — the optimal mix is where the lines cross | 🎲 |
| Mixed Strategies: Expected Value | Set opponent indifferent — choose your mix so they can't exploit your pattern | 🎲 |
| Ch 4. Non-Zero-Sum Games | ||
| Non-Zero-Sum Intro | When payoffs don't sum to zero, cooperation and conflict coexist | 🎲 |
| Prisoner's Dilemma and Chicken | Two games that define modern game theory — and why rational self-interest can be collectively irrational | 🎲 |
| Volunteer's Dilemma | Everyone benefits if someone acts, but acting is costly — who volunteers? | 🎲 |
| Repeated Prisoner's Dilemma | Play once: defect. Play forever: cooperate. The shadow of the future changes everything | 🎲 |
📺 Video lectures: Yale ECON 159: Game Theory (Ben Polak)
Neighbors
- 🎰 Probability — mixed strategies are probability distributions over pure strategies
- 💰 Economics — Nash equilibrium and mechanism design connect
- 📐 Linear Algebra — game matrices and minimax theorem use linear programming
- 🏷 Auction Theory — auctions as a class of mechanism design problem
- Applied:
power diagrams in ad auctions and one-shot bidding strategy