brinkmanship (n.)
also brinksmanship, with parasitic -s- and construction based on salesmanship, sportsmanship, etc.; from brink (the image of the brink of war dates to at least 1840).

Associated with the policies advocated by John Foster Dulles (1888-1959), U.S. Secretary of State 1953-1959. The word springs from Dulles' philosophy as outlined in a magazine interview [with Time-Life Washington bureau chief James Shepley] early 1956:
The ability to get to the verge without getting into the war is the necessary art. If you cannot master it, you inevitably get into war. If you try to run away from it, if you are scared to go to the brink, you are lost.
The quote was widely criticized by the Eisenhower Administration's opponents, and the first attested use of brinkmanship seems to have been in such a context, a few weeks after the magazine appeared, by Democratic presidential candidate Adlai Stevenson criticizing Dulles for "boasting of his brinkmanship, ... the art of bringing us to the edge of the nuclear abyss."