Directly opposing someone whose personality is oriented around competing and winning tends to trigger exactly the defensive, escalating resistance that makes cooperation harder to reach. An alternative approach reframes the conflict as a bargain, giving the other person a real way to keep pursuing what they want while also meeting specific, concrete conditions — working with the underlying drive to win, rather than trying to defeat it outright.
This isn't capitulation; it's a deliberate strategic choice, and it works specifically because it offers something the other person actually values (continued pursuit of their goal) in exchange for something they'd otherwise resist giving up entirely, which is a structurally easier ask than requesting they simply abandon what they want.