How are you forming these teams? Ad-hoc? Then I would have no allegiance. But if you assign people with birthdays on odd days to one team and even to another then I can see tribal behavior and competition emerging. You have to some reason to assign people to team no matter how arbitrary.
Getting to the point: How about if people gave physical stuff (old xbox games? whatever it is that would excite your community) and winners could choose from this? That way people can share, recycle, compete in a virtuous cycle.
I feel that it would be tough for you o/w to find ways to make enough money to give people $ for points/activity. At the point that the conversion from virtual to real becomes meaningful to them it is bound to bankrupt you because they are taking more value out than putting in. Second Law of Thermodynamics and all that*
* unless there are network effects...