No, it’s best to never get in to it in the first place—once you bid even $1, you can come out worse than you started (losing the bid), but if you never bid, you just break even.
If never giving up really is the best strategy, then you can assume they’ll use it. If they’re using it, it’s better to give up now. If you assume they use a mixed strategy in which they have a chance of giving up, it really doesn’t matter what you do, as is often the case with Nash equilibria, but you have to use the same mixed strategy or they’d change theirs.
You don’t know when the other person will give up and it’s better to be the last person to give up.
No, it’s best to never get in to it in the first place—once you bid even $1, you can come out worse than you started (losing the bid), but if you never bid, you just break even.
If never giving up really is the best strategy, then you can assume they’ll use it. If they’re using it, it’s better to give up now. If you assume they use a mixed strategy in which they have a chance of giving up, it really doesn’t matter what you do, as is often the case with Nash equilibria, but you have to use the same mixed strategy or they’d change theirs.