Game theory is a way to understand how people make decisions when they are in a situation where they have to think about what others will do. It is like playing a game where you need to think about what the other players might do to win.
Game theory is a study of how people make choices. It helps us understand how people can work together or compete with each other. This is important in many areas like economics, politics, and everyday life.
There are different types of games in game theory. Here are some common ones:
Let's look at some simple examples to understand game theory better:
Imagine two friends, Alice and Bob, are caught for a crime. They are kept in separate rooms and cannot talk to each other. The police offer them a deal:
What should Alice and Bob do? If they both think only about themselves, they might both confess and get 5 years in jail. But if they trust each other and stay silent, they only get 1 year in jail. This shows how game theory helps us understand decisions.
Imagine a couple, John and Mary, want to go out for the evening. John wants to watch a football game, and Mary wants to go to a concert. They both want to be together but also want to do what they like. They have to decide:
They need to find a way to make a decision that makes them both as happy as possible. This is another example of game theory in action.
Game theory is used in many real-world situations:
Here are some important concepts in game theory:
A Nash Equilibrium is a situation where no player can do better by changing their strategy if the other players keep their strategies the same. It is named after John Nash, a famous mathematician.
For example, in the Prisoner's Dilemma, if both Alice and Bob confess, they are in a Nash Equilibrium because neither can do better by changing their decision alone.
A dominant strategy is the best choice for a player, no matter what the other players do. If a player has a dominant strategy, they will always choose it.
In the Prisoner's Dilemma, confessing is a dominant strategy for both Alice and Bob because it gives them a better outcome no matter what the other does.
A mixed strategy is when a player chooses different actions with certain probabilities. This is used when there is no clear best choice.
For example, in a game of rock-paper-scissors, players might use a mixed strategy by choosing rock, paper, or scissors randomly to keep their opponent guessing.
Game theory helps us understand how people make decisions in different situations. It shows us how cooperation and competition work in economics, politics, and everyday life. By studying game theory, we can learn to make better choices and understand the choices of others.
Key points to remember:
