what is nash equilibrium 
nash equilibrium is a concept in game theory where the game reaches an optimal outcome this is a state that gives individual players no incentive to deviate from their initial strategy the players know their opponent s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player overall an individual can receive no incremental benefit from changing actions assuming that other players remain constant in their strategies a game may have multiple nash equilibria or none at all jiaqi zhou investopediaunderstanding nash equilibriumnash equilibrium is named after its inventor john nash an american mathematician it is considered one of the most important concepts of game theory which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves the reason why nash equilibrium is considered such an important concept of game theory relates to its applicability the nash equilibrium can be incorporated into a wide range of disciplines from economics to social sciences to quickly find the nash equilibrium or see if it even exists reveal each player s strategy to the other players if no one changes their strategy then the nash equilibrium is proven nash equilibrium vs dominant strategynash equilibrium is often compared to dominant strategy both being strategies of game theory the nash equilibrium states that the optimal strategy for an actor is to stay the course of their initial strategy while knowing the opponent s strategy and that all players maintain the same strategy dominant strategy asserts that the chosen strategy of an actor will lead to better results out of all the possible strategies that can be used regardless of the strategy that the opponent uses all models of game theory only work if the players involved are rational agents meaning that they desire specific outcomes operate in attempting to choose the most optimal outcome incorporate uncertainty in their decisions and are realistic in their options both terms are similar but slightly different nash equilibrium states that nothing is gained if any of the players change their strategy while all of the other players maintain their strategy dominant strategy asserts that a player will choose a strategy that will lead to the best outcome regardless of the strategies that the other players have chosen dominant strategy can be included in nash equilibrium whereas a nash equilibrium may not be the best strategy in a game example of nash equilibriumimagine a game between tom and sam in this simple game both players can choose strategy a to receive 1 or strategy b to lose 1 logically both players choose strategy a and receive a payoff of 1 if you revealed sam s strategy to tom and vice versa you see that no player deviates from the original choice knowing the other player s move means little and doesn t change either player s behavior outcome a represents a nash equilibrium julie bang investopediaprisoner s dilemmathe prisoner s dilemma is a common situation analyzed in game theory that can employ the nash equilibrium in this game two criminals are arrested and each is held in solitary confinement with no means of communicating with the other the prosecutors do not have the evidence to convict the pair so they offer each prisoner the opportunity to either betray the other by testifying that the other committed the crime or cooperate by remaining silent if both prisoners betray each other each serves five years in prison if a betrays b but b remains silent prisoner a is set free and prisoner b serves 10 years in prison or vice versa if each remains silent then each serves just one year in prison in this example the nash equilibrium is for both players to betray each other even though mutual cooperation leads to a better outcome if one prisoner chooses mutual cooperation and the other does not one prisoner s outcome is worse 