This whole ant allegory is ridiculous to anyone who has studied ants in any detail.
A Queen ant holds no power in a colony. In fact, it's almost the other way around. The workers drag her around, by force, to wherever they feel she should be. The queen is just a breeding machine. All she does, every day, is lay eggs. Except for the times that she is resting, being fed, or hibernating, thats it.
Foraging for protein and nitrogen rich foods is prompted by the presence of hungry larva in the colony. Foraging for high sugar foods happens constantly regardless of the presence of a queen. The drive to expand the colony by tunneling is driven by the population of the colony. A colony doesn't react specifically to the queen being threatened, but by the colony as a whole being threatened, as they react in the same way regardless of the presence of a queen.
Despite popular belief, workers are not genetically inferior to the queen. They share the same genetic code (with the exception that the queen is using sperm from a seperate colony to fertilize the eggs). It is believed that hormones transfered from the workers to the larva during feeding and grooming prompt the larva to develop into gynes (Winged female reproductives).
Long story short, there is no power structure in an ant colony. None at all. If anyone could be said to have any control at all it would be the developing larva, as they have the ability to command the workers to fetch food.
Ant's have a form of group mind, where every individual acts like a single neuron in a very small brain. A single ant is absolutely retarded, but 5000 ants are brilliant.
I've often thought that a true free market economy would function in much the same way.
...
To address the original post, I believe it much depends on the amount of psychological control. For instance, the Asians could be brainwashed into believing that the American is a god, or god-like, and that their afterlife depended on their performance in his servitude. The American could even push it further and convince them that the gun was magical and prevent the Asians from learning how to make one.
Of course that doesn't apply well to the real world that we are trying to describe with this exercise, but perhaps they could be brainwashed into believing that the work is in some other way 'for their own good' like by preventing unemployment...