IPA: /ˈbrɪŋk.mən.ʃɪp/
KK: /ˈbrɪŋkˌmænʃɪp/
The act of taking risks in a dangerous situation to gain an advantage, especially in politics or negotiations.
The two countries engaged in brinkmanship, each trying to outdo the other in their threats.
Brinkmanship is formed from "brink" (from Old English "brynca", meaning edge or border) and "-manship" (from Old English "-scipe", meaning the art or skill of). The term refers to the art of bringing a situation to the edge of disaster to achieve a favorable outcome.
Think of being at the 'edge' ('brink') of a situation and using skill ('-manship') to navigate it — that's what brinkmanship means.
No commonly confused words.