\begin{definition}[Definition:Dominating Strategy]
Let $G$ be a game.
Let player $P$ have pure strategies $A_1$ and $A_2$ in $G$.
Then $A_1$ '''dominates''' $A_2$ {{iff}}:
:for any strategy of an opposing player, $A_1$ is at least as good as $A_2$
:for at least one strategy of an opposing player, $A_1$ is strictly better than $A_2$.
\end{definition}