# What Is Game Theory Example?

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Martha Robinson

Game Theory Example: Understanding the Concept

Game Theory is a mathematical theory that deals with decision-making in strategic situations. It is a study of how people behave in situations where their actions affect others and vice versa. Game theory has wide applications in various fields such as economics, political science, psychology, and biology.

## Prisoner’s Dilemma

One of the classic examples of game theory is the Prisoner’s Dilemma. In this scenario, two suspects are arrested for a crime and questioned separately. They are given two options – to confess or remain silent.

• If both confess, they both get a prison sentence of 5 years each.
• If one confesses and the other remains silent, the one who confesses gets no prison time while the other gets a sentence of 10 years.
• If both remain silent, they both get a sentence of 1 year each for a lesser charge.

The dilemma arises because each prisoner must decide whether to betray their partner or not. If one betrays while the other remains silent, then the betrayer goes free while the other gets a longer sentence. If both betray, then they both get a longer sentence than if they had remained silent.

### Payoff Matrix

To understand this scenario better, we can use a payoff matrix to show the possible outcomes for each player.

Player B
Player A C D
D E F

In this matrix, C represents confessing while D represents remaining silent. E and F are the payoffs for each player depending on their decision and the decision of the other player.

### Nash Equilibrium

The Nash Equilibrium is a concept in game theory that describes a state in which no player can improve their outcome by changing their strategy given the other player’s strategy. In this scenario, the Nash equilibrium is for both players to confess since neither player can improve their outcome by changing their decision.

Game theory provides insights into how people make decisions in strategic situations. The Prisoner’s Dilemma is just one example of how game theory can be applied to real-life situations where decisions made by one person can affect others. By understanding game theory, we can make better decisions in our personal and professional lives.