kingmake

To use one's influence to help someone else into a position of political power.

Okay, you get on the extension in the other room and listen to me kingmake Percy President.

"Sol thinks of himself as a kingmaker," she said. "And actually, I suppose he is — " "Why doesn't he kingmake something for himself?"

To play so as to cause another player to win.

I do dislike it if part of the skill of playing consists of manipulating the people who are out of the running to get them to kingmake for you.

If they really can't, they recognize they're kingmakers, and if there's a good reason they kingmake, but even then they usually deal with their predator to buy time and bang on their prey a bit (you never know - now and again it works).