DEFINITION: The notion of a “Nash equilibrium” is a key concept within the mathematical discipline of game theory.
Widely applied in economics, the Nash equilibrium describes the solution of a certain type of non-cooperative game involving two or more players.
A Nash equilibrium comes about in circumstances in which no player has a motivation to alter its initial strategy. In other words, all players feel that the outcome is optimal.
More specifically, even when each player learns of its opponents’ strategies, all players continue to regard their initial choice as their best strategy.
ETYMOLOGY: The Nash equilibrium was introduced by mathematician John Forbes Nash, Jr., in a paper published in 1950.[1]
The paper was based on work Nash was doing at Princeton University on his doctoral dissertation, entitled “Non-cooperative Games.” He received his PhD in mathematics from Princeton that same year (1950).
Nash was awarded the Nobel Memorial Prize in Economic Sciences in 1994 for his work on game theory.
It is sometimes said that Nash’s result was anticipated in an 1838 discussion of oligopoly by French mathematician, Antoine Augustin Cournot. However, Nash’s work was much broader, effectively laying the foundations for the entire field of game theory.
The English word “equilibrium” is attested from the early seventeenth century.
It derives from the Latin noun aequilibrium, with the same meaning, from the adjective aequilibris, aequilibre, meaning “level.” The latter word is compounded of the adjective aequus, meaning “equal,” and the noun libra, meaning “a pair of scales.”
USAGE: In general terms, a Nash equilibrium is a situation in which an individual gains no additional advantage by altering its actions. The solution assumes that the other players maintain consistent strategies.
A given game may possess either numerous Nash equilibria or none.
The reason why the concept of Nash equilibrium has attracted so much attention and is considered so important is that it may be applied to many fields of social science, although its utility for the discipline of economics in particular probably remains its best-known application.
Moreover, it is quite simple to determine whether a given game-theoretic solution is or is not a Nash equilibrium: simply reveal each player’s strategy to the others.
If no player alters its strategy and the status quo ante is maintained, then the solution constitutes an instance of the Nash equilibrium.
Note
1. John F. Nash, Jr. (1950) “Equilibrium Points in n-Person Games,” Proceedings of the National Academy of Sciences. USA, 36: 48–49.