equilibrium point

A Nash equilibrium of a strategic game is a profile of strategies (s_1^*, ..., s_n^*), where s_i^* element S_i (S_i is the strategy set of player i), such that for each player i, for all s_i element S_i, u_i(s_i^*, s_(-i)^*)>=u_i(s_i, s_(-i)^*), where s_(-i) = (s)_(j element N\{i}) and u_i :S congruent ×_(j element N) S_j->R. Another way to state the Nash equilibrium condition is that s_i^* solves max_(s_i element 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" of the television crime drama NUMB3RS mentions Nash equilibrium.