[ZetaZero]

picking 1 would still dominate over any other strategy, in a head-to-head.

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.

[StevenWaterman]

For a short intuitive proof of that 1st sentence, imagine both players pick 1 every time. You both lose 1 point. If you're tied for score, you're still tied after the round.

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.

[HWR_14]

This is only true if your goal is to have a score higher than your opponent. It's not true if your goal is to have the highest possible score.

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.

[theptip]

> This is only true if your goal is to have a score higher than your opponent

That is what “dominant” in game theory means, which was the specific claim that’s being discussed.

[HWR_14]

No you are incorrect in what a "dominant" strategy means. It has nothing to do with dominating your opponent.

[theptip]

A dominant strategy in game theory means it's your best strategy, regardless of what strategy your opponents pick.

> 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.