What Is Nash Equilibrium?

Nash equilibrium is a concept in 澳洲幸运5官方开奖结果体彩网:game theory where the game reaches a stat꧙e that gives individual players no incentive to deviate from their initial strategy. The players know their opponents' strategy and can't deviate from their chosen strategy because it remains optimal.

Thus, if all players use their optimal strategies, an individual can receive no incremental benefit from changing actions, assuming that other players remain 𒁃constant in their strategies. A g𝓰ame may have multiple Nash equilibria or none at all.

Understanding Nash Equilibrium

Nash equilibrium is named after its inventor, 澳洲幸运5官方开奖结果体彩网:John Nash, an American mathematician. It is co💜nsidered 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 re🍸lates 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 i𝔉t even exists, reveal each player’s strategy to the other players. I𝔉f no one changes their strategy, then the Nash equilibrium is proven.

Nash Equilibrium vs. Dominant Strategy

Nash equilibrium is often compared to dominant strategy, 澳洲幸运5官方开奖结果体彩网:both bꩵeing strategies of game theo💖ry. The Nash equilibrium states that the optimal strategy f🍃or an actor is to stay the course of their strategy whil﷽e knowing the opponent’s strategy, and that all players maintain the same strategy.

Dominant s🉐trategy 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.

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 th൩at will lead to the best outcome regardless of the strategies that the other players have chosen.

Example of Nash Equilibrium

Imagine 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 Tom's to Sam's, each would likely maintain strategy A because neither has an option to change to a strategy that would benefit them more. Knowing the other player’s move means little and doesn’t change either player’s behavior. Outcome A represents a Nash equilibrium.

Prisoner’s Dilemma

The prisoner’s dilemma is a common situation anౠalyzed in game theory that demonstrates the Nash equilibrium. In this game, two criminals are arrested and each is held in solitary confinement wi꧂th 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 remain silent.

If both prisoners betray each other, each serves five years in prison. If A betrays B but B remains silent, prisoner A is ဣset free and prisoner B serves 10 years in prison, and vice versa. If each remains silent, 🥀then each serves just one year in prison.

In this example, the Nash ꧑equilibrium 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.

The Bottom Line

The Nash equilibrium is a component of game theory that 🀅asserts that a player will continue with their chosen strategy while knowing their opponent’s strategy, as they have no incentive to change course.