In modern mobile networks with multiple network operators, distributed access points, and many users, the efficient utilization of available bandwidth merits consideration. A game theory approach is used here. It envisions a three-layer system in which each network operator runs multiple base stations that connect to second-level access points. Clients connect to the access points to receive network services. In normal situations, some clients will demand more bandwidth than others. It would be more efficient for those with lower demands to share their available bandwidth with others. Hence, the model creates a third layer of network provision by having certain clients become interim access points. This helps smooth out bandwidth distribution and reduces the chance that a primary access point becomes saturated by direct client connections.

Because there are multiple network operators, one must assume different pricing mechanisms. One must also assume that a sharing client may suddenly demand more bandwidth, thus interrupting the endpoint client receiving shared bandwidth. All these considerations lead to an optimization problem that uses a double Stackelberg game as the model.

The authors develop a mathematical description of the model, and then implement in MATLAB to run simulations. The impressive results show improved network utilization. However, I have a couple of comments on the analysis. First, during the mathematical development, there is the comment, “Note that the higher-order terms are not convex and including them in the approximation process increases the complexity. In other words, the higher-order terms are negligible in comparison to the one of the first-order.” The second sentence does not follow from the first. It fails to show why the higher-order terms are negligible; rather, one more likely infers that the terms are discarded for convenience. Second, there will be a certain overhead imposed on the mobile devices participating in this system, such as iteratively calculating the new optima in the sharing scheme as the environment evolves. It would be appropriate to discuss the cost in terms of compute power and possibly battery life in the client devices, even if only to note that such costs are negligible or that this should be done in another paper.