In the Nash equilibrium, each player's strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome they desire. The prisoners' dilemma is a common game theory example and one that adequately showcases the effect of the Nash equilibrium.
Nash equilibria need not exist if the set of choices is infinite and non-compact. An example is a game where two players simultaneously name a number and the player naming the larger number wins.
A Nash Equilibrium in game theory is a collection of strategies, one for each player in a social game, where there is no benefit for any player to switch strategies. In this situation, all players the game are satisfied with their game choices at the same time, so the game remains at equilibrium.
A Nash equilibrium is. reached when each player chooses the best strategy for himself, given the other strategies chosen by the other players in the group. A situation in which each firm chooses the best strategy given the strategies chosen by other firms is called a. Nash equillibrium.