Another thought might be Diplomacy. Obviously you can’t model actual Diplomacy – that would be insanely complex, and probably illegal – but you could do a little schematic of interactions. Something like this:
Germany, Austria, England, France, and Italy each start with 3 territories. There are 6 unclaimed territories at the beginning.
Every turn, one player can ATTACK another, SUPPORT another, or EXPLORE.
Resolution of attacks: if the combined strength of the ATTACKing player and everyone SUPPORTing them exceeds the combined strength of the player who has been attacked and everyone SUPPORTing them, the attacked player loses one territory and the attacker gains one. If not, no change.
If you EXPLORE and no one ATTACKs you, you get one unclaimed territory, as long as there is one left and enough to go around. If there are more EXPLORing players who are not ATTACKed than there are unclaimed territories, no one gets an unclaimed territory.
Example: England and France decide to go after Austria. Austria and Germany make an agreement to go after France, but Germany decides to betray Austria instead. Italy explores.
Turn 1: France attacks Austria. England supports France. Austria attacks France. Germany explores. Italy explores.
Resolution: France’s attack on Austria is 6 (England + France) to 3 (Austria). Austria’s attack on France is 3 to 6. France gains 1 territory from Austria. Germany and Italy get one unclaimed territory each.
Now: France has 4, England has 3, Austria has 2, Germany has 4, Italy has 4, there are 4 unclaimed.
Austria decides to get Italy to help take its revenge against Germany. Germany attacks Austria. France and England continue to go after Austria; now it’s England’s turn to try to get a territory.
Turn 2: England attacks Austria. France supports England. Germany attacks Austria. Austria supports Italy. Italy attacks Germany.
Resolution: England’s attack on Austria has a strength of 7 (3 for England + 4 for France) against 2. Italy’s attack on Germany has a strength of 6 (4 + 2 from Austria) against 4. Germany’s attack on Austria has a strength of 4 against 2. All attacks succeed. Austria loses 2, Germany stays the same (gaining 1 from Austria, losing 1 to Italy), England gains 1, Italy gains 1.
Now: England has 4, France has 4, Italy has 5, Germany has 4, Austria has 0 and is eliminated! There are still 4 unclaimed.
I suppose that if there were more successful attacks against a side than the side had territories, there’d have to be some rule about who wins first – probably the strongest attack. (If three sides had attacked Austria, they could only lose two territories.)
Anyway, maybe this won’t do at all, but it seems to me as though it could give you a lot of scope for bringing various kind of motivations in play. One player will mercilessly strive for revenge against anyone who betrays her, one player will ally with you in exchange for some out-of-game fetch item, one player will always strive to take down the person in the lead, that sort of thing.