I'm not talking about people not participating because they're lazy, I'm talking about people not participating because there is nothing to do.
So long as there is at least one other person who doesn't have everything they want, there's something to do. I can live with the possibility that one person might not get everything they want.
So by that definition, circle jerking will feed everyone.
I know you said they can earn the $1 off someone else and use that to buy the food from the controller of food, but there's only so much the controllers of food needs (or has time to consume), and that's the problem. Once he has all the $ in circulation, where will the more dollars come from without an army backed inflation currency?