Bridging the gap between big data and game theory: A general hierarchical pricing framework

In this paper, we propose a general pricing framework, helping the controller promote agents to achieve its objective, for a big data network with one controller and a large number of agents. The convergence of the framework is guaranteed for a general class of objective functions: a separable convex function for the controller and a convex function for each agent. Specially, the proposed framework can converge linearly, when the controller's objective is strongly convex, and the agents' objectives have a uniform Lipschitz gradient. The convergence, and especially the linear convergence is not dependent on the number of agents, which is important for a network with large size. Through numerical results, we apply our pricing framework in a wireless virtualized network to verify its fast convergence, where the pricing framework converges after just a few steps.