In my mind, the best way to discuss bargaining comes from Michael Scott in "The Office." When trying to negotiate a buyout of the his company, he rejects the first offer without even hearing it. When one of his colleagues asks him why, his analysis is simple: "Always reject the first offer." It is this premise of compromising and ensuring that your interests are met in the process of bargaining that makes it so difficult. It's a challenge for it to not be adversarial as both sides seek to bring out their own sense of the subjective in negotiations. The challenge is that both subjective visions fundamentally compete with one another. Within bargaining, I see a point where both sides have to comprehend that a good solution might be better than a perfect one that completely matches their subjectivity. It is this moment, where both sides can understand that what they are receiving from "the other" is far superior than nothing at all and bargaining is the process where both sides can fully recognize this moment and act on it without letting it pass by unnoticed.
Obviously it depends very much on what kind of bargaining you are talking about whether it is a child bargaining with a parent for more ice cream or a later bed time or a giant union bargaining with a corporation about salaries and benefits.
But in some ways, they must all start with an offer and a counter offer. Once two positions are established, either side can make compromises in order to come closer to an agreement. Of course who makes the compromises depends in large part on who is in the position with the most power at the start of the negotiations.
Once the sides get close enough together to strike a deal, an agreement or bargain is reached.