What Is a Game?

students, welcome to Game Theory 🎯. In this lesson, you will learn what a “game” means in economics and other social settings, why people’s choices can depend on what others do, and how game theory helps us study those situations. By the end, you should be able to define game theory as the study of strategic interaction, recognize when decisions are interdependent, and tell the difference between a strategic problem and a standard optimization problem.

Introduction: Why do other people’s choices matter?

Imagine you are choosing what time to leave for school. If you leave early, you avoid traffic. That is a normal decision problem: you choose one action and get one outcome, mostly based on your own choice. Now imagine you are on a team project, and your grade depends not only on your work but also on whether your teammates do their part. Suddenly, your best choice depends on what other people will do. That is the basic idea behind a game in game theory 🤝.

Game theory is the study of strategic interaction. A strategic interaction is a situation where the result for each person depends on the choices of others as well as their own choices. This happens in economics, politics, sports, business, and daily life.

A few key questions guide this topic:

What makes a situation “strategic”?
When do people have interdependent decisions?
How is a game theory problem different from a normal optimization problem?

These questions matter because many real-world decisions are not made in isolation. If you are deciding whether to buy a new phone plan, a company is deciding whether to lower prices, or two candidates are deciding how to campaign, each choice can change the outcome for everyone involved.

What game theory studies

Game theory looks at situations where each decision-maker is called a player. A player can be a person, a company, a country, or even a group. Each player has possible actions, often called strategies. A strategy is a plan for what to do in a situation.

The important feature is that one player’s outcome depends on what the others choose. In many cases, each player tries to choose the best action while thinking about how others will react. This is what makes the situation strategic.

For example, consider two coffee shops on the same street. Each shop can choose to charge a high price or a low price. If both charge high prices, both may earn good profits. But if one charges low and the other charges high, the low-price shop may attract more customers. Each shop’s profit depends on the other shop’s decision. That is a strategic setting.

Game theory does not only study conflict. It also studies cooperation, bargaining, voting, matching, and teamwork. Some games have winners and losers, while others involve shared benefits or shared losses. The common feature is interdependence.

What makes a situation strategic?

A situation is strategic when the following are true:

There are at least two decision-makers.
Each decision-maker has choices.
The outcome for each decision-maker depends on the choices of others.
People understand, at least partly, that their decisions affect one another.

This can happen even in very ordinary situations.

Everyday examples

Choosing a restaurant 🍔: You want sushi, but your friend wants pizza. If you choose together, your final decision depends on each person’s preference.
Traffic lanes 🚗: If many drivers switch lanes at once, congestion changes. Your travel time depends on what other drivers do.
Studying for a group exam 📚: Your success may depend on both your own study time and your classmates’ preparation if you share notes or work in a study group.
Sports strategy ⚽: A soccer player’s best shot depends on the goalkeeper’s position.

In each example, the outcome is not determined by one person alone. That is why these are strategic situations.

Strategic problems vs. standard optimization problems

It is useful to compare strategic problems with standard optimization problems.

In a standard optimization problem, one decision-maker chooses the best action given a set of constraints. The environment is usually treated as fixed. For example, if students is trying to spend as little money as possible on a bus ride, the goal might be to pick the cheapest route. The best choice depends on the available options, but not on another person actively changing their behavior in response.

In a strategic problem, however, the “environment” includes other decision-makers who are also choosing actions. Your best decision depends on what you expect them to do, and their best decision depends on what they expect you to do.

This creates a feedback loop 🔄.

Simple comparison

Optimization problem: Find the best choice when the situation is mostly fixed.
Strategic problem: Find the best choice while other people are also trying to choose well.

For example, suppose you are picking the fastest route home. If traffic is already fixed, that is a standard optimization problem. But if thousands of drivers are deciding routes at the same time, your choice affects and is affected by theirs. Then it becomes a game theory problem.

Mathematically, optimization often looks like choosing $x$ to maximize a function $f(x)$. In a strategic setting, your payoff may look more like $u_i(s_i, s_{-i})$, where $s_i$ is your strategy and $s_{-i}$ represents the strategies of everyone else. The key difference is that your outcome depends on others’ decisions too.

Core terminology you need to know

To understand the rest of the course, students, you should be comfortable with a few core terms.

Player

A player is any decision-maker in a game. Players do not have to be people. They can also be firms, political parties, or countries.

Strategy

A strategy is a choice or plan of action. Sometimes a strategy is a single move, and sometimes it is a full plan for what to do in different situations.

Payoff

A payoff is the result a player gets from a combination of choices. It may represent money, votes, happiness, time saved, or another measure of success.

Best response

A best response is the best action for a player, given what the other players are doing or expected to do. If another player chooses strategy $s_j$, your best response is the strategy that gives you the highest payoff.

Interdependence

Interdependence means that one person’s outcome depends on another person’s action. This is the heart of game theory.

These terms will appear again and again, so it helps to see them in a real example.

Example: Two stores choosing prices

Suppose two stores sell the same snack near a school. Each store can choose a high price or a low price. If both choose high prices, each store earns a decent profit because students have fewer cheap alternatives. If one store chooses low and the other chooses high, the low-price store may get more customers. If both choose low prices, profits may fall because they compete too hard.

This situation is strategic because each store’s profit depends on both choices.

Let the stores be Player $1$ and Player $2$. Their strategies might be $H$ for high price and $L$ for low price. The outcome for Player $1$ depends on the pair $(s_1, s_2)$, where $s_1$ is Player $1$’s strategy and $s_2$ is Player $2$’s strategy.

If Player $1$ thinks Player $2$ will choose $H$, then Player $1$ may prefer $L$. But if Player $1$ thinks Player $2$ will choose $L$, the answer may change. That is exactly why game theory is useful: it helps us study choices that depend on expectations about others.

Examples from economics, politics, and everyday life

Game theory shows up in many places.

Economics 💼

Firms choose prices, output levels, advertising, or product quality while watching competitors. A company’s profit depends not just on its own decision but also on what rivals do. That is why competition is often strategic.

Politics 🗳️

Candidates choose messages, campaign locations, and policy positions while reacting to opponents. A candidate may change a speech depending on what the other candidate said. Voters, parties, and governments all interact strategically.

Everyday life 👥

People negotiate chores at home, decide whether to join a group project, or choose when to merge in traffic. Even choosing whether to send a text message first can be strategic if the other person’s response matters.

Sports 🏀

A basketball player decides whether to pass or shoot based on defenders’ positions. A tennis player chooses where to serve based on the opponent’s expected return. These are strategic moves because the best action depends on an opponent’s action.

How to tell if a problem is a game

A good test is to ask:

Are there multiple decision-makers?
Does each person’s result depend on what others do?
Do people care about anticipating one another’s actions?

If the answer is yes, the situation is likely a game theory problem.

If the answer is no, then it may just be a standard choice problem.

Here is a quick example:

Choosing how much homework time to spend tonight may be a personal optimization problem.
Choosing whether to study alone or in a group, when your classmates’ choices affect the outcome, is more strategic.

The more a situation involves reacting to others, the more game theory becomes useful.

Conclusion

students, game theory is the study of strategic interaction. It helps us understand situations where decisions are interdependent, meaning that one person’s outcome depends on what others do. This is different from a standard optimization problem, where one decision-maker chooses the best action in a mostly fixed environment.

You have also learned the basic language of game theory: player, strategy, payoff, best response, and interdependence. These ideas are the foundation for analyzing competition, cooperation, bargaining, and many other real-world situations. In the next lessons, you will use these tools to study how people make decisions when they must think about one another.

Study Notes

Game theory is the study of strategic interaction.
A strategic situation has at least two decision-makers whose outcomes depend on each other’s choices.
A player is any decision-maker, such as a person, firm, or country.
A strategy is a plan or choice of action.
A payoff is the result a player receives from the combination of choices.
A best response is the best choice for a player given the choices of others.
Interdependence means one person’s outcome depends on another person’s decision.
Standard optimization problems involve choosing the best option in a mostly fixed environment.
Strategic problems require thinking about what others will do and how they will react.
Game theory applies to economics, politics, sports, business, and everyday life.