Large-Scale Mechanism Design for Networks: Superimposability and Dynamic Implementation

Network utility maximization (NUM) is a fundamental framework for optimizing next-generation networks. However, self-interested agents with private information pose challenges due to potential system manipulation. To address these challenges, the literature on economic mechanism design has emerged. Existing mechanisms are not suited for large-scale networks due to their complexity, high implementation costs, and difficulty to adapt to dynamic settings. This paper proposes a large-scale mechanism design framework that mitigates these limitations. As the number of agents $I$ approaches infinity, their incentive to misreport decreases rapidly at a rate of $\mathcal {O}(1/I^{2})$. We introduce a superimposable framework applicable to any NUM algorithm without modifications, reducing implementation costs. In the dynamic setting, the large-scale mechanism design framework introduces the decomposability of the problem, enabling agents to align their own interests with the objectives of the dynamic NUM problem. This alignment helps overcome the additional, more stringent incentive constraints encountered in dynamic settings. Extending our results to dynamic settings, we present the design of a Dynamic Large-Scale mechanism with desirable properties and the corresponding Dynamic Superimposable Large-Scale mechanism. Our numerical experiments validate the fact that our proposed schemes are approximately $I$ times faster than the seminal VCG mechanism.