A Nash equilibrium of a strategic game is a profile of strategies , where ( is the strategy set of player ), such that for each player , , , where and .

Another way to state the Nash equilibrium condition is that solves for each . In words, in a Nash equilibrium, no player has an incentive to deviate from the strategy chosen, since no player can choose a better strategy given the choices of the other players.

The Season 1 episode "Dirty Bomb" (2005) of the television crime drama NUMB3RS mentions Nash equilibrium.

Portions of this entry contributed by Andreas Lonbørg

Nash, J. F. "Non-Cooperative Games." Ann. Math. 54, 286-295, 1951.

CITE THIS AS:

Lonbørg, Andreas and Weisstein, Eric W. "Nash Equilibrium." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NashEquilibrium.html