Game-Theory

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? ...

Voting Theory: Why Democracy is Mathematically Impossible In 1952, economist Kenneth Arrow proved something shocking: There is no perfect voting system. Any method of aggregating individual preferences into collective decisions must violate at least one desirable property. Arrow’s Impossibility Theorem isn’t just an abstract mathematical curiosity — it explains: Why elections often feel unfair Why third-party candidates “spoil” elections Why strategic voting is rational Why democracies struggle with consistency Welcome to voting theory — where mathematics reveals the fundamental limitations of democracy. ...

Evolutionary Game Theory: How Strategies Survive and Spread Why do animals fight with ritualized displays instead of killing each other? Why do bacteria cooperate sometimes and defect other times? Why do humans feel guilt, reciprocate favors, and punish cheaters — even when it’s costly? Evolutionary game theory answers these questions by applying game theory to evolution. Instead of assuming rational players, it asks: Which strategies survive and spread over time? ...

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. ...

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. ...