This is not an insurmountable problem by any means. Group competition occurs on a variety of levels. Nations compete. Ethnic groups compete. Political parties compete. Businesses compete. Individuals compete. When competing as groups, there just need to be benefits shared among the group (i.e. a reason for people to be a part of the group) and ways to punish free-riding (i.e. ways to prevent people from receiving the benefits of the group while not contributing to the group).
The point I'm making, though, is that if any of those entities chooses not to compete with other like entities, it will dwindle into irrelevance or die out. That entity will not be making the world a better place by choosing not to compete. Instead it will simply be replaced by other such entities which are more inclined to put their own interests first, as has happened to countless other nations, ethnic groups, political factions, businesses, and individuals that did not compete successfully for whatever reason.
But this results in kinda a chicken&egg problem: If nobody cooperates then we are wasting resources and effort, but if only some people cooperate they put themselves in a disadvantageous position, compared to the remaining competitors, and will have a hard time pulling trough.