# Nash Equilibrium in Game Theory: Examples and Prisoner’s Dilemma

## Nash Equilibrium in Game Theory: Examples and Prisoner’s Dilemma

In game theory, Nash equilibrium is a concept that represents a stable state in a game where no player has an incentive to change their strategy, given the strategies of the other players. It is named after John Nash, who introduced the concept in his 1950 paper “Equilibrium Points in N-Person Games”. Nash equilibrium is widely used in various fields, including economics, political science, and biology.

In game theory, Nash equilibrium is a concept that describes a stable state in a game where no player has an incentive to change their strategy, given the strategies of the other players. It is named after John Nash, who introduced the concept in his 1950 paper “Non-Cooperative Games”. Nash equilibrium is widely used in various fields, including economics, political science, and evolutionary biology.

At Nash equilibrium, each player’s strategy is the best response to the strategies chosen by the other players. In other words, no player can unilaterally deviate from their strategy and improve their outcome. This does not mean that Nash equilibrium leads to the best possible outcome for all players; it only guarantees that no player can improve their situation by changing their strategy.

In the Prisoner’s Dilemma, the Nash equilibrium occurs when both suspects confess. This is because, regardless of what the other suspect does, each suspect’s best response is to confess. If one suspect remains silent while the other confesses, the silent suspect risks receiving the harshest sentence. Therefore, both suspects confess, resulting in a moderate sentence for both.

## Examples of Nash Equilibrium

Nash equilibrium is a concept in game theory that describes a stable state in which no player has an incentive to change their strategy. It is named after mathematician John Nash, who introduced the concept in his seminal paper in 1950.

Here are some examples of Nash equilibrium in different scenarios:

1. Price Competition: Consider two companies competing in the same market. Each company can choose a price for their product, and the customers will choose the company with the lower price. If both companies set the same price, they will split the market equally. If one company lowers its price, it will capture a larger market share. However, if both companies lower their prices, they will enter into a price war and both will suffer. The Nash equilibrium occurs when both companies set the same price, as neither has an incentive to deviate from this strategy.

These examples illustrate the concept of Nash equilibrium and how it applies to different situations in game theory. Nash equilibrium provides a valuable tool for analyzing strategic interactions and predicting outcomes in various competitive scenarios.