Devastation (also published as "Virtual War") by Gloria Skurzynski
The earth’s population has been decimated by disease and natural disasters—and those who remain live in domed cities, sealed off to prevent the spread of further devastation. In eighteen days, there will be a bloodless, virtual war between the few remaining world powers with the winner to take possession of the only place on Earth still safe to live undomed—a remote tropical island in the Pacific.