The incentive for the operator of a private city would be profit: offering an attractive product at the right price. This would likely include public goods, such as a clean environment, police, and fire protection, as well as some infrastructure and social rules. But the operator’s main service is to ensure that the free order is not disturbed and that residents’ life and property are secure.
Competition has been proven as the only effective method in human history for limitation of power. In a private city, contract and arbitration are efficient tools in favor of the residents. But ultimately, it is competition and the possibility of a speedy exit that guarantee that the operator remains a service provider and does not become a dictator.
A private city is not a utopian, constructivist idea. Instead, it is simply a known business model applied to another sector, the market of living together.