In everyday life, a game is something you play for fun. In economics and mathematics, a game is any situation where people's outcomes depend on the choices of others. It’s the study of strategic decision-making.

Think of two coffee shops on the same street. If one shop lowers its prices, it affects the other shop's sales. This is a strategic interaction. To analyze it, we need to know three things:

Game theory uses these components to model how rational people behave when their fates are intertwined.

Games can be broadly split into two categories based on whether players can make binding agreements.

Cooperative games are situations where players can negotiate and form alliances. They can sign contracts and trust that others will hold up their end of the bargain. The main question here is how to fairly divide the spoils of cooperation. For example, if two companies decide to jointly develop a new technology, they can create a legal partnership to share the costs and profits.

Non-cooperative games, on the other hand, are where players cannot form binding agreements. Each player must make their own decisions, anticipating what the others will do. Our coffee shops are in a non-cooperative game. They might verbally agree to keep prices high, but there's nothing stopping one from secretly offering a discount to steal customers. Most of what we study in game theory falls into this category, as it models competition in markets, politics, and even biology.

In a non-cooperative game, how can we predict what will happen? We look for a state of balance, where no one has an incentive to change their mind. This is called a Nash Equilibrium.

The classic example is the Prisoner's Dilemma. Imagine two partners in crime are arrested and held in separate interrogation rooms. They can't communicate. The prosecutor offers each of them the same deal:

Let's map this out in a payoff matrix. The numbers represent the prison sentence (a negative payoff).

Consider it from Prisoner A's perspective. She doesn't know what Prisoner B will do.

• "If B stays silent, my best move is to confess (0 years is better than 1 year)."
• "If B confesses, my best move is still to confess (5 years is better than 10 years)."

No matter what B does, A is better off confessing. Since the situation is identical for Prisoner B, he will also reason that confessing is his best strategy.

The result is that both prisoners confess and get 5 years. This is the Nash Equilibrium. Neither prisoner can improve their own situation by changing their mind alone. If Prisoner A decided to stay silent while B confesses, she would get 10 years instead of 5.

Notice the paradox: if they could have cooperated (and trusted each other), they both would have stayed silent and only served 1 year each. But because they acted in their own individual self-interest, they ended up with a worse outcome for the group.

Let's check what you've learned about these core concepts.

Understanding these basic building blocks—players, strategies, payoffs, and the Nash equilibrium—allows us to analyze countless strategic interactions in the world around us.