I have a suggestion - Design the Game which tigers use when they chase a deer, how they manage to keep the competition out and only compete with their prey the deer. My hunch is that you may have to use variables outside the realms of non-cooperative Game Theory to model such predatory behaviour, but it happens in nature.
S.K.Mallick,
for S.K.Mallick, S.Raychaudhury, S.Mallick and others