# Nash Equilibrium – Definition

### Nash Equilibrium Definition

The Nash equilibrium is a popular gaming theory that was developed by John Forbes Nash, a mathematician. This theory presents the optimal solution in a game where both players are non-cooperative due to lack of incentive to change their plans or strategy. According to the Nash equilibrium, despite that each player is perceived to know the opponent’s strategies, there are unwilling to change their initial strategy since there is nothing to gain by changing their strategy. Hence, both players stick to their initial strategies, rather than switching to a new strategy.

### A Little More on What is the Nash Equilibrium

Nash equilibrium is a concept that maintains that when players of a game perceive that there is no benefit they can derive from changing their actions or strategies, they maintain their initial strategy throughout the game, despite that they are aware of the opponent’s strategy. In a game, it is possible to have no nash equilibrium or have multiple nash equilibrium.

Given that players in a game strive to get what is best for them in a game, the inventor of the nash equilibrium, John Nash developed the gaming concept. Hence, when there is no incentive or benefit of changing a strategy, players do not deviate from the original plan. The nash equilibrium is not limited to the gaming industry, it can be applied in various disciplines.

The belief of  a player that he has nothing to gain by changing his strategy, even after being aware of the opponent’s strategy gave rise to the development of the Nash equilibrium. According to this gaming theory, each player wins by not deviating from the initial strategy, all the players get their desired result. The Nash equilibrium is largely proven if players do not deviate from their initial strategy after each player’s technichique is shown to the other players. No deviation occurs since there is no incentive attached to changing their strategy.

### Prisoner’s Dilemma

A popular game used to exemplify the Nash equilibrium is the prisoner’s dilemma. A prisoner’s dilemma is a scenario in which there are two criminals kept in different custodies and both have no means to talk to each other. Due to lack of evidence by the prosecutor, the prosecutor meet each of the prisoners and tells them to betray each other or tells one not to talk about the crime and the other suspect testifies against the one that is silent.

It is vital to know that if both parties choose to betray each other, they are served jail term and if one betrays the other, one is set free and the silent one spends time in prison. However, if they both decide to remain silent on the matter, they will both serve a year in prison. In this example, cooperation between the two will give a better outcome but since the suspects see that they will gain by betraying the other, they are likely going to betray each other.