# Nash Equilibrium

What is the Nash equilibrium’

A Nash equilibrium is a concept in the framework of game theory where the optimal outcome in a game where there is no incentive to deviate from its original strategy. More specifically, a Nash equilibrium is a concept from game theory where the optimal outcome of the game, when no player has incentive to deviate from chosen strategy after considering an opponent’s choice. In General, the individual may receive additional benefits from changing actions, assuming other players remain constant in their strategies. The game can have several Nash Equilibria or none at all.

Breaking down the ‘Nash equilibrium’

Nash equilibrium is named after its inventor, John Nash, an American mathematician. It is one of the most important concepts of game theory that attempts to determine mathematically and logically the actions that players must take in order to achieve the best results for yourself. Therefore, the Nash equilibrium is a very important concept of game theory is associated with its applicability. The Nash equilibrium can be included in a wide range of disciplines, from Economics to social Sciences.

Nash Equilibrium

Nash equilibrium is the solution to a game in which two or more players have a strategy, and each participant, given the opponent’s choice, he has no incentive, nothing to gain, by switching his strategy. In the Nash equilibrium strategy of each player is optimal when considering the decisions of other players. Each player wins because everyone gets the results they desire. To quickly check if a Nash equilibrium exists, to disclose the strategy of each player to the other players. If no one changes its strategy, then the Nash equilibrium is proven.

For example, imagine a game between Tom and Sam. In this simple game players can choose the strategy that to get \$1, or strategy B to lose \$1. Logically, both players choose a strategy and get a payoff of \$1. If you have identified the strategy of the Sam with Tom and Vice versa, you see that a player deviates from the initial selection. Knowing the move of the other player means little, and does not change the behavior of any player. The final document represents a Nash equilibrium.

The prisoner’s dilemma

The prisoner’s dilemma is a common situation analyzed in game theory that can be used by a Nash equilibrium. In this game, two criminals are detained, and each was held in solitary confinement without the possibility of communication with others. The prosecution has no evidence to condemn this couple, so they offer each prisoner the opportunity either to betray the other, testifying that the other committed the crime or cooperate with silence. If both prisoners betray each other, each serves five years in prison. If a betrays B But B remains silent prisoner A And B are served in captivity 10 years of imprisonment, or Vice versa. If a friend is silent, each serves for only one year in prison. The Nash equilibrium in this example for both players to betray each other. Although mutual cooperation yields a better result, if one prisoner chooses mutual cooperation and the other not, one a prisoner, the result is worse.