Im just reading Thomas Schelling's Theory of Conflict and one of his key tenets is that providing an identifiable point around which the discussion can be centered will tend to lead the discussion to be centered around that (classical anchoring). However, he brings out that in many cases, having a "line in the sand" brings benefits to all sides by allowing intermediate deals to be struck when only extremes were possible before.

This article, however, clearly demonstrates that having a line in the sand can be just as bad as it can be good, as it is with all of biases. However, I really recommend Schelling hit on "what is good" (in the evolutionary sense) about this phenomenon.