Negotiations happen every day. People negotiate pretty much anything and everything. It's often quite casual, in a form that we might not even notice, but often it's formal as well, especially in a software project context.
The number, clarity, and feasibility of requirements, bug accuracy, and severity, availability of resources, priority of features, go-live date, release schedule, overall cost, and price, are all usual negotiation points. The agreed figure at the end is rarely, if ever, the original baseline.
For our purposes, and ease of illustration, let's just say there are only two parties involved: a supplier and a customer. As a manager, you will need to understand and appreciate the art of negotiation from both angles.
As the saying goes: An old poacher makes the best gamekeeper.
Empathy is a skill often associated with negotiation...