The second offer does not have to be real. If it's real, what's the point of negotiating with the first company?
If you are not willing to work for $X, simply saying that you want $1.25X won't work, but mentioning a hypothetical competitive offer might. If it doesn't, well, you weren't going to take the job (for $X) in either case anyway.
If you're slaving in interviews and only have one offer, I can see why the offer is compelling. In this current market, I totally get it. But just a couple short years ago, the parent poster's approach was probably sound.
Lol people explicitly directly ask to see offer letters. Bluffing like this is a great way to actually have the negotiations end prematurely because you're found to be operating in bad faith.
and you tell them that the company do not want their offer to be revealed due to confidentiality reasons. The first employer would need to take your word for it. And if they deem you lying, they can always stand hard on their offer, and risk losing the candidate.
I have shared them with my current employer to let them know the market and what I was considering.