Spatial games and global optimization for mobile association problems

The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various mathematical, economical, and control theory phenomena, such as Witsenhausen’s counterexample in stochastic control theory, principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we focus on mobile association problems: the determination of the cells corresponding to each base station, i.e., the locations at which intelligent mobile terminals prefer to connect to a given base station rather than to others. This work combines game theory and optimal transport theory to characterize the solution based on fluid approximations. We characterize the optimal solution from both the global network and the mobile user points of view. Part of this work has been presented at the 49th IEEE Conference on Decision and Control. Alonso Silva and Eitan Altman are with INRIA. Email: [email protected] Hamidou Tembine and Mérouane Debbah are with Supélec. Email: [email protected]