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Turn on the charm. Coax and cajole.
Persuasion is a Charisma Skill.
The higher your Charisma Score, the more likely you will succeed on Persuasion Checks.
As of Early Access Patch 9, Persuasion skill also affects the prices offered by Traders alongside their Attitude value towards the hero talking to them.
The formula to calculate purchase prices from Traders is
ItemValue * (2.5 - Persuasion/10 - Attitude/200)
They will buy wares from the player for
ItemValue / (2.5 - Persuasion/10 - Attitude/200)