This is my favorite tip. I have been using this for 20+ years, and it usually goes something like, "If you offer me $145,000/year, 15% annual bonus, 15% LTI and a $10,000 signing bonus, I will give my two weeks notice with no chance for a competitive offer.
Anything less, and it's a conversation."
(This is an exact example from 15+ years ago).
They came back with no signing bonus (I had to ask!) but bumped me up to 20% bonus and 20% LTI (stock options).
I said, "yes" immediately.
In another situation, I was coming from a government job to a private sector job. I studied what the limits were to the government coming up with a competing offer.
For my prospective new job, I gave them a number and was blunt: This is $40k above my current salary. This is $1000 more than my current organization can counter with, unless they go directly to [government head] to get approval."
Since that process would take weeks, if you meet this number I will give two weeks notice immediately.
I was offered (and took) both positions.
Secondary lesson: Negotiating when you are already employed gives you an upper hand.