2 people want to kill each other. The one taking the first step is the intelligent one because according to your definition he was better at predicting an outcome than his opponent.
The real world is more complex than that and there are multiple options where both survive, or letting your opponent live and killing yourself because his life is more beneficial to humanity and so on.
Any organism can survive, but for most (including us) that implies a selfish outlook but the most intelligent people I know or heard of never even consider their own ego.