\begin{definition}[Definition:Nash Equilibrium]
Let a strategic game $G$ be modelled by:
:$G = \stratgame N {A_i} {\succsim_i}$
A '''Nash equilibrium''' of $G$ is a profile $a^* \in A$ of moves which has the property that:
:$\forall i \in N: \forall a_i \in A_i: \tuple {a^*_{-i}, a^*_i} \succsim_i \tuple {a^*_{-i}, a_i}$
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.
{{NamedforDef|John Forbes Nash|cat = Nash}}
\end{definition}