Agreed. I wasn't describing the problem clearly at all, it is just a rough idea. Now, I agree that the problem is only interesting if we keep some constraints,

Agreed. I wasn't describing the problem clearly at all, it is just a rough idea. Now, I agree that the problem is only interesting if we keep some constraints, a) at least as to how people can move and possibly also on b) what information people have on the strategy of the opposing team, as well as c) how teams can coordinate among their own members. Another fun constraint would be to model mixed democrate/republican households of different sizes that can only move together.