Is there a word for the phenomenon of knowing a compromise will happen and intentionally overbending the truth so the conclusion is more truthful?

Is there a word that describes the phenomenon of compromise where side A is telling the truth, side B is outright lying, but because both sides don't want the arbiter to pick dead in the middle, rather closer to their side, they exaggerate their case so that the concluded middle ground is actually favorable to them?

It comes up in politics, arguments, design, budget, etc. Would be great if there were a word to describe it.

It's a gaming of the arbiter's strategy "the truth is in the middle"

I wasn't successful in looking it up through any reverse dictionaries since it requires a situation and perspective of a situation to understand, and I don't have the English skill to explain it without an example. But I hope there's a word for it! (I would think there's definitely a word for it in Chinese. Chinese seems to always have very terse words for complex situational phenomenons. But I don't know the word in Chinese either.)

Tough bargaining, for one. Overstating your case in order to settle favorably is covered by many sayings and figures of speech, but hardly a single precise word.