Game theory uses maths to study strategy. Game theory studies more than just board games, sports, and games of luck. It also studies things like business and military decisions. In game theory, people call all of these situations "games." In other words, you can use game theory to study any situation where more than one person makes choices.
The players in a game are not even always people. Players can be people, companies, armies, dogs or other things. Each player wants something: maybe a company wants to make as much money as it can, or a country wants to win a war. Sometimes the players work together, but often they are competing against each other.
Game theory is part of economics.
Prisoner's Dilemma [change]
One important game is the prisoner's dilemma. It's an imaginary situation that shows why sometimes people do not cooperate (help each other).
Imagine this situation: the police catch two criminals after they committed a crime. The police do not know which person committed the crime and which person just helped. They question the two in separate cells. Each prisoner can either stay silent or betray (hurt) the other by blaming the crime on them. If both stay silent, they only go to jail for 6 months. If one betrays and the other stays silent, the one that stays silent goes to jail for 10 years and the other one does not go to jail at all. If they both betray each other, they each go to jail for 2 years. No matter what happens, the prisoners will never see each other again.
If you are a prisoner in this situation and you only care about yourself, the way to get the smallest sentence is to betray the other prisoner. No matter what, you get a shorter sentence when you betray than when you do not. If the other prisoner stays silent and does not betray, then betraying means you do not go to jail at all instead of going to jail for 6 months. If the other prisoner betrays, then betraying lets you go to jail for 2 years instead of 10 years. In other words, it's always best for you to betray, even though the two of you would be better off if you both stayed silent. It is said that betraying the other prisoner is your "dominant strategy" because it is always the best thing for you to do, no matter what the other prisoner does.
The prisoner's dilemma is like a lot of other situations in the real world. For example, if two countries are trying to decide whether to make new weapons, they are both better off if neither country does. But sometimes the countries are in the same situation as the prisoners: each country only cares about itself, and it's better off if it "betrays" the other country by making weapons.
The prisoner's dilemma does not have same result if some of the details are different. If the prisoners (or countries) can talk with each other and plan for the future, they might both decide to cooperate (not betray) because they hope that will make the other country help them in the future. In game theory, this is called a "repeated game." If the players are altruistic (if they care about each other), they might be OK with going to jail so they can help the other person.