Of two or more people or groups, to be engaged in ferocious, pernicious competition with one another. It's a symptom of the society we live in that we're all trained to cut one another's throats just to earn a little bit more money. The majority of the economy is dominated by a few megacorporations, while all the smaller businesses are cutting one another's throats for what little market share is left over. Those two want the promotion so badly that they're willing to cut one another's throats to get it.