We are all negotiators; with our customers, our vendors, our employees, and our families.  Negotiation traditionally boils down to each party taking a firm stance on an issue. Each side states—and re-states—their position, until one side makes concessions, or they come to an impasse and give up. The problem with this is that the more we clarify our positions, the more committed we become to them. Our identity becomes tied to the positions we take. So when one party compromises their position; egos are bruised, and relationships are damaged. There is a more effective approach. 

When Negotiating, Focus on Interests, Not Positions

Avoid making statements about your positions at all if possible. Instead, focus on what each party really wants, and what they are really concerned about. Often you can find a solution that meets both parties interests, which may not be so incompatible with each other after all. 

Excerpt from "Getting to Yes: Negotiating Agreement Without Giving In" by Roger Fisher and William Ury is a concise and useful guide to the psychology of negotiation.