However, if you are trying to maximize your H2H score against a pool of contestants, a cooperation strategy, where you both alternated taking the lower number would be close to optimal.
Now imagine you change your number to stop ties. Well now you've picked a number bigger than 1, and you lose every time. If you were tied, now you're losing.
If ties are with 0, you always choose 1 in either situation. If ties are worth -1, choosing 1 always achieves a greater than or equal to score but the number will be much lower than if you some percentage of the time choose another number.
That is what “dominant” in game theory means, which was the specific claim that’s being discussed.
> https://en.wikipedia.org/wiki/Strategic_dominance
> In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play.
That is what is being described above.