[Post completely edited for symmetry reasons:]
Well, this is for 6...but I am interested in 7.
What about this one:
A hunts C,D
B hunts D,E
C hunts E,F
D hunts F,G
E hunts G,A
F hunts A,B
G hunts B,C
So A is hunted by E&F, both being hunted by C who is A's prey...
So each nation needs to hunt the hunter of its own hunters. Furthermore, there are no 4-cycles and each nation is contained in a 3-cycle.
Therefore, alliances are highly unstable. The game is also likely to end very soon once the first nation got killed, so sitting back and developing is severly discouraged by this victory condition!
Diplomacy, on the other hand, rules, since it is unimported who killed the killed nations.
(Note that I am merely talking about victory conditions and do not intend to place any other restrictions on alliances, etc. Every player is just assigned his own private mission!)
Does this make sense to obtain a good game? I figured that 4-cycles must be prohibited so that there are no obvious alliances, while 3-cycles rule out alliances easily.
What else would be good rules for such a victory-condition?
Here is a picture showing above's hunting relation for 7 players:
