Intermediate

Auction Theory: The Mathematics of Bidding Wars In 1994, the U.S. government auctioned radio spectrum licenses using game theory. The result? $7.7 billion in revenue — far more than expected. In 2000, the UK’s 3G telecom auction raised $34 billion using carefully designed rules. In 2016, the FCC’s broadcast incentive auction was called “the most complex auction ever conducted” — a reverse auction followed by a forward auction, designed by game theorists. ...

Backward Induction: Solving Games by Working Backwards You’re playing chess. How do you decide your next move? Master players don’t just think one move ahead — they think many moves ahead, anticipating their opponent’s responses, then their own responses to those responses, and so on. This is backward induction — one of game theory’s most powerful techniques. Instead of reasoning forward from the start, you reason backward from the end. ...

Mixed Strategies: Why You Should Be Unpredictable You’ve learned about dominant strategies and Nash equilibria in pure strategies. But what happens when there’s no pure strategy Nash equilibrium? What if being predictable is your worst enemy? Welcome to the world of mixed strategies — where randomness becomes your most powerful weapon. The Problem with Being Predictable Imagine you’re a goalkeeper facing a penalty kick. You can dive left or right. The striker can shoot left or right. If you both go the same way, the striker scores. If you guess correctly, you save. ...

Repeated Games: How Cooperation Emerges from Self-Interest In the Prisoner’s Dilemma, rational players defect. In the Tragedy of the Commons, rational actors destroy shared resources. One-shot game theory seems to paint a bleak picture: selfishness always wins. But real life isn’t a series of one-shot games. We interact with the same people, companies, and countries repeatedly. And this changes everything. Welcome to repeated games — where cooperation emerges not from altruism, but from enlightened self-interest. ...

The Tragedy of the Commons: When Self-Interest Destroys Everything Imagine a village where everyone shares a common grazing field. Each villager rationally decides to add one more cow to maximize their profit. Each individual decision makes sense. But collectively, they destroy the field that sustains them all. This is the Tragedy of the Commons — one of the most important concepts in game theory, economics, and environmental science. It explains why rational individuals often destroy the very resources they depend on. ...

The Ultimatum Game: Are Humans Really Rational? Imagine this: I give you $100 and ask you to propose how to split it with a stranger. There’s one catch — if the stranger rejects your offer, neither of you gets anything. Game theory predicts you’ll offer $1 and keep $99. After all, $1 is better than $0, so the stranger should accept. In reality? Most people offer $40-50, and offers below $30 are frequently rejected. ...