Game-Theory

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. ...

Why does everyone in the United States drive on the right side of the road? Not because it’s better than driving on the left—the British drive on the left and do just fine. We drive on the right because everyone else drives on the right. This is a coordination game—a situation where the key is not beating others, but matching them. These games are everywhere, and they reveal fascinating insights about how societies form conventions, standards, and norms. ...

Imagine a game where one strategy is best no matter what your opponent does. You don’t need to predict their behavior, guess their intentions, or outthink them. You just pick the dominant strategy and you’re done. This is the simplest situation in game theory—and when you have a dominant strategy, your decision becomes trivial. Let’s understand this powerful concept. What is a Dominant Strategy? A dominant strategy is a strategy that gives you a better outcome than any other strategy, regardless of what your opponents do. ...

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. ...

Imagine you and a partner are arrested for a crime. The police separate you into different rooms and offer each of you the same deal. You can’t communicate. You don’t know what your partner will do. And the choice you make will determine whether you go free or spend years in prison. Welcome to the most famous problem in game theory: the Prisoner’s Dilemma. It reveals a disturbing truth about rational decision-making that explains everything from climate change to price wars to why your office kitchen is always dirty. ...

Have you ever wondered why gas stations on the same corner charge similar prices? Or why countries engage in arms races even though both would be better off spending less on weapons? Or why you and your friends can’t decide where to eat, even though everyone wants to go somewhere? These situations all involve strategic decision-making—and that’s exactly what game theory studies. What is Game Theory? Game theory is the mathematical study of strategic interactions. It’s a framework for understanding situations where your best choice depends on what others choose, and their best choice depends on what you choose. ...

In poker, every dollar you win comes from someone else’s loss. In chess, one player wins and one loses. In tennis, your point is your opponent’s lost opportunity. These are zero-sum games—pure competition where one player’s gain equals another’s loss. Understanding zero-sum games changes how you compete, negotiate, and think about conflict. Let’s explore this fundamental concept. What is a Zero-Sum Game? A zero-sum game is a situation where the total gains and losses always sum to zero. Whatever one player wins, another must lose. ...

When most people hear the word “game,” they think of fun activities like chess, poker, or video games. But in mathematics, a “game” has a much broader and more precise meaning. Game theory studies strategic situations where the outcome depends not just on your choices, but on the choices of others too. What Makes Something a “Game”? In game theory, a game is any situation where: Multiple decision-makers (called “players”) interact Each player has choices (called “strategies”) they can make Each combination of choices leads to an outcome with specific rewards or costs (called “payoffs”) Players care about these outcomes and try to make rational decisions The beauty of this definition is that it applies to far more than board games. Business competition, political negotiations, evolutionary biology, and even social dilemmas are all “games” in the mathematical sense. ...

If you want to master game theory, you need to master payoff matrices. They’re the single most important tool for analyzing two-player games, and once you understand them, you’ll see strategic situations everywhere. A payoff matrix is simply a table that shows every possible outcome of a game and what each player gets in each scenario. But this simple visualization unlocks powerful insights about human behavior, business strategy, and why rational people sometimes make seemingly irrational choices. ...