Any time you make a decision where the result depends on someone else's choice, you're playing a game. This could be as simple as deciding which movie to see with a friend or as complex as a company setting prices to compete with a rival. Game theory is the study of these strategic situations.

At its core, every game has three basic components:

1. Players: The decision-makers involved. There must be at least two.
2. Strategies: The possible actions each player can take.
3. Payoffs: The outcomes or consequences for each player, resulting from their combined choices. Payoffs can be anything from money to points to simple satisfaction.

Game theory provides a framework to analyze how players make choices to achieve the best possible payoff for themselves.

Games generally fall into two categories based on how the players can interact.

Cooperative Games: Here, players can form alliances and make binding agreements. The focus shifts from individual strategy to what groups can achieve together. Examples include business partners negotiating a contract or countries forming a trade agreement. The analysis is about how to fairly distribute the rewards of cooperation.

To analyze a game, we need a way to see all the possible outcomes at a glance. The most common tool for this is a payoff matrix. It’s simply a table that shows the payoffs for each player for every possible combination of strategies.

Let's imagine a simple game. Two friends, Alex and Ben, want to meet up. Alex can go to the Library, and Ben can go to the Cafe. They'd both rather be together than alone. We can map this out.

In the table below, Alex's choices are the rows, and Ben's are the columns. The first number in each cell is Alex's payoff, and the second is Ben's. A higher number is better. We'll give them 10 points for meeting and 0 for being alone.

This matrix makes it easy to see the consequences of each decision. If Alex chooses Cafe and Ben chooses Cafe, they both get their best outcome. If Alex chooses Cafe and Ben chooses Library, they both end up alone and get nothing.

Game theory makes a big assumption: players are rational. This doesn't mean they're always smart or correct. It means two things:

1. They act to maximize their own payoff.
2. They know that all other players are also acting to maximize their payoffs.

This assumption of rationality is the engine that drives the analysis. It allows us to predict how players will behave. If Alex knows Ben is rational, he can anticipate that Ben will try to go to the same place Alex does. This mutual understanding of self-interest is what makes game theory a powerful tool for understanding strategic interactions.