Definition:Nash Equilibrium

Definition
Let a strategic game $G$ be modelled by:
 * $G = \left\langle{N, \left\langle{A_i}\right\rangle, \left\langle{\succsim_i}\right\rangle}\right\rangle$

A Nash equilibrium of $G$ is a profile $a^* \in A$ of moves which has the property that:
 * $\forall i \in N: \forall a_i \in A_i: \left({a^*_{-i}, a^*_i}\right) \succsim_i \left({a^*_{-i}, a_i}\right)$

Thus, for $a^*$ to be a Nash equilibrium, no player $i$ has a move yielding a preferable outcome to that when $a^*_i$ is chosen, given that every other player $j$ has chosen his own equilibrium move.

That is, no player can profitably deviate, if no other player also deviates.