What do you do when a motorist refuses to take their right-of-way?

My local culture values politeness above competence, and it can be a source of stress. It is also a car-centric town and the drivers don't seem to think it's condescending to freeze up and donate their right-of-way to anybody not in an automobile. The behavior is common but not predictable so you never know when your idea of movement is going to be flouted by an act of excessive kindness. I never know what to do and it's frustrating.