Proposed concepts of operations for advanced air mobility rely on private service providers being responsible for providing air traffic management services to uncrewed aircraft such as drones and autonomous air taxis. While such proposals are unprecedented in the aviation context, one can draw parallels to the Internet and the role played by Internet service providers in managing web traffic. A study of the evolution of the Internet illustrates that, without clear rules for cooperation around a nascent market, private profit motives incentivize against service provider cooperation, especially for traffic flows that traverse multiple regions managed by different service providers. To address this problem, we propose a profit-sharing mechanism based on the Shapley value that incentivizes service providers to cooperate. We show that this mechanism i) ensures that service providers route flights along globally optimal routes, and ii) encourages service providers to work together in providing more efficient routes. We study the allocation of sectors to service providers and show that different allocations can cause large differences in profit earned. Finally, we discuss some of the remaining challenges with having a federated network of private service providers supporting traffic management for advanced air mobility operations.