Indeed.
"You two couldn't share the island; so now NO-ONE gets it!"
It's the proven way of sorting out arguments.
Why did they have to argue over it anyway? I'm sure there would be scientific interest, but from the point of view of a sovereign state it's a lump of rock in the middle of nowhere. The study of such is something for the international community, leaving the claims being for the valuable deposits of... eh.... rock?