Is there a name for coop-games with possible betrayal?

My playgroup generally likes coop games, but me and one other friend would also like to (sometimes) have a clear winner.

Are there any games, where you work towards a common goal, that you have to achieve or the whole group looses. But one player may also sabotage/betray the group to come out the sole winner? Does this kind of game have its own genre/keyword to look for?