TOPICS
Search

Nash Equilibrium


A Nash equilibrium of a strategic game is a profile of strategies (s_1^*,...,s_n^*), where s_i^* in S_i (S_i is the strategy set of player i), such that for each player i,  forall s_i in S_i, u_i(s_i^*,s_(-i)^*)>=u_i(s_i,s_(-i)^*), where s_(-i)=(s)_(j in N\{i}) and u_i:S=×_(j in N)S_j->R.

Another way to state the Nash equilibrium condition is that s_i^* solves max_(s_i in S_i)u_i(s_i,s_(-i)^*) for each i. 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.


See also

Nash's Theorem

Portions of this entry contributed by Andreas Lonbørg

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Nash Equilibrium

Cite this as:

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

Subject classifications