My best negotiation trick, which I’ve frequently used, is called anchoring. It’s best highlighted by an example…
Ok, I want to buy something, and a fair price is $2,000, the offer price is $2,400. I’ll go in and make a semi-joke that I want to buy it for $300 and mention that figure repeatedly, with a big smile to keep it friendly. Suddenly even $1,600 suddenly seems reasonable because it’s being compared to with the joke $300 and I’ll offer $1,400, and at least go for $1,600.
Had I not done this $2,400 would be in everyone’s mind, and even $2,000 would have seemed like a low offer.
One more example - if you’re on $5k per month, tell your boss, as a joke, that you should be on $20k for all the work you do - mention it a few times, with a smile every time. Now, ask for a $1k pay rise - sounds like peanuts.
Sometimes the joke may not be appropriate, in which case you still need to make sure whatever figures are mentioned suit your goal. So if you want to haggle for that $40,000 car, at least have the courage to start with $32,000 with a serious face. It just makes the seller struggle to get anywhere near $40,000. But if you start with $38,000 you’ve already lost half the battle.