A Unified Game-Theoretic Framework for Discrete Power Minimization in Wireless Networks

This paper proposes a unified noncooperative game for discrete power minimization in wireless networks. We prove that the proposed game, with a carefully chosen payoff function, falls into the framework of potential games where pure strategy Nash equilibrium (NE) exists. The feasibility of the pure strategy NE is guaranteed with properly designed penalty functions and penalty factors. It is revealed that the optimal solution to the sum discrete power minimization problem constitutes a pure strategy NE of the proposed game under mild conditions. Also, we prove that the pure strategy NE of the proposed game is also the optimal solution to the sum discrete power minimization problem under some particular conditions. An iterative algorithm is then devised to obtain the pure strategy NE. Two examples which can be solved efficiently by using our framework are also provided.