Economics

In medieval England, villages had common grazing land-the “commons”-where all villagers could graze their sheep. Each shepherd faced a decision: How many sheep should I graze? The logic was simple: Adding one more sheep: I get 100% of the profit Cost of overgrazing: Shared among all shepherds So every rational shepherd added more sheep. And more. And more. Until the commons was destroyed. Overgrazed. Barren. Worthless to everyone. This wasn’t malice. Each shepherd was acting rationally in their own self-interest. ...

In March 2000, the NASDAQ peaked at 5,048-more than double its value from a year earlier. Companies with no revenue, no profits, and often no viable business model were worth billions. Pets.com spent $27 million on advertising (including a Super Bowl ad) and collapsed nine months after its IPO. Webvan raised $800 million to deliver groceries. It shut down after burning through all the money in less than two years. ...

Cooperative Game Theory: How to Split the Pie Fairly Three friends start a company together. After five years of hard work, they sell it for $10 million. How should they split the money? Equal shares? ($3.33M each) Proportional to hours worked? Based on who contributed what? What if one person brought the key technology, another the business connections, and the third the execution? Cooperative game theory provides mathematical answers to these questions. ...

Stackelberg Competition: The Advantage of Moving First In chess, moving first is a small advantage. In business, moving first can be worth billions. Amazon dominated e-commerce by moving first Google captured search by moving first Facebook dominated social networking by moving first But moving first isn’t always good: Microsoft’s Zune failed against the iPod Google+ failed against Facebook Many “first-mover” startups fail while fast followers succeed When does moving first help? When does it hurt? ...

Mechanism Design: Engineering Games with Desired Outcomes In 2012, Alvin Roth and Lloyd Shapley won the Nobel Prize in Economics for mechanism design - the art of reverse-engineering game theory. Instead of analyzing existing games, mechanism design asks: Can we design the rules to get the outcome we want? The result? Kidney exchange networks that save thousands of lives Spectrum auctions that raised $100+ billion for governments School choice systems that match students to schools fairly Voting systems that resist manipulation Mechanism design is game theory’s most powerful application - turning abstract mathematics into real-world systems that align incentives and produce efficient outcomes. ...

Signaling Games: Communication When Words Are Cheap Why do peacocks have such ridiculously large tails? Why does a college degree help you get a job, even if you learned nothing useful? Why do companies spend millions on Super Bowl ads that don’t describe their products? Signaling theory provides the answer: When words are cheap, credible communication requires costly signals. From biology to business, from education to dating, signaling games explain how information is transmitted when one party knows more than another - and has an incentive to lie. ...

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. ...

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. ...

John Nash won the Nobel Prize for an idea so simple you can explain it in 5 minutes. Yet this idea revolutionized economics, predicted Cold War outcomes, explains why you’re stuck in traffic, and even helps explain evolution. Let’s understand Nash Equilibrium-the most important concept in game theory. The Core Idea (In One Sentence) A Nash Equilibrium is a situation where no player can improve their outcome by changing their strategy alone-everyone is doing the best they can given what everyone else is doing. ...

Here’s one of the most unsettling discoveries in mathematics: perfectly rational players, each acting in their own self-interest, can all end up worse off than if they had acted irrationally. This isn’t a flaw in game theory-it’s a feature of reality that game theory reveals. This paradox explains traffic jams, arms races, overfishing, climate change negotiations, and why businesses sometimes engage in destructive price wars. Understanding it will change how you see human cooperation (and its failures). ...