When two parties cannot find an immediate way forward on a decision that requires mutual agreement, they enter negotiations. Generally, the parties go back and forth until a resolution is finalised which is somewhere near half-way of what each wanted. Both parties are happy (or as good as it is going to get) and they move forward. This is often termed a win-win agreement.
Crisis negotiations are no different. When confronted with a barricaded criminal, a mentally impaired person or someone who is suicidal, a crisis negotiator will ask what the person is trying to achieve and why. Once known, the negotiator will then find a mid-way point to work towards.
To benefit the most from negotiations, one party must have some leverage or 'power' over the other which is termed bargaining power. In crisis negotiations, which is undertaken by law enforcement personnel, the leverage is freedom. Their tactic is to cordon, contain, and voice appeal. During the negotiation the officer will work on a way forward by using reason, rationale, and the fact that the other party is contained and can't go anywhere until the event is resolved.
In civil negotiations, this is not the case. Both parties are free to leave, free to say no, free to stand their ground. So how do you come to an agreement? By seeing things from the other party's perspective. This will show you what is important to them and you can work on this aspect. It may be something as simple as the need to save face, to appear to be the winner. It could be something so personal that they are ready to forgo other requests.
In your next negotiation, see things from the other party's perspective first and and work on that when you reach an impasse. You will soon have a win.