Brinkmanship is pushing a situation to the point of disaster without quite going over the edge. Brinkmanship is mainly a political policy.
When you're on the brink of something, you're right on the edge. In politics, brinkmanship is an approach in which a country pushes a situation extremely close to a dangerous point. Many considered the Cold War between the U.S. and Russia an example of brinkmanship; the accumulation of so many deadly weapons could have led to disaster. Brinkmanship is a gamble: by coming close to a dangerous outcome, you hope to get an agreement or concession you wouldn't otherwise get.