Maybe that would feel to much like playing on your own, and not seem very fun. If you could give each “player” an indentifiable characteristic it might be bring out some weird psychologycal effects. Either something kind of abstract like red v blue, or something more anthropomorphic like boy v girl.

There is Babylon 5 episode about the conflict between Drazi of "green" and "purple" characteristic (2x03, coincidently? one of the more important episodes for the overall story arc). Last week I was reminded of this while thinking about Ingress and it's green vs. blue "conflict" (which is wonderfully designed such that taking the in-game fights into meatspace will gain you nothing in comparison to settling them in-game).

I can't help but think of the Byzantine factions, the Blues and the Greens.

In a riot sparked by a chariot race[0], half of Constantinople was destroyed.

[0] https://en.wikipedia.org/wiki/Nika_riots