Nash equilibrium

In game theory, a Nash equilibrium exists when no player has an incentive to change their strategy when the game is iterated, provided no other player changes their strategy either.

The name comes from their discoverer, John Nash.

It is common for games to have more than one Nash equilibrium.

A very simple example of a game with Nash equilibria is:

It is fairly obvious that if one player chooses x then so should the other. Similarly, if one player chooses y then so should the other.

 

If the game is repeated, then each player will be able to form expectations about the other's choices and will follow. Therefore the players will both choose the same one of x or y and stick to their choice. The two Nash equilibria are both players choosing x and both players choosing y.

Nash equilibria occur in economics and finance, for example in some exchange rate theory.